3 added 6 characters in body

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain; and then output the result.

To make what I'm asking slightly clearer, here's a javascript program that does it, but, at 782 bytes, it's not very well golfed yet:

var primes=[2,3];
function nextPrime(){
var n=2;
while(isAMultipleOfAKnownPrime(n)){n++}
primes.push(n);
}
function isAKnownPrime(n){return primes.indexOf(n)!=-1};
function isAMultipleOfAKnownPrime(n){
for(var i=0;i<primes.length;i++)if(n%primes[i]==0)return true;
return false;
}
function primeFactorize(n){
while(primes[primes.length-1]<n)nextPrime();
if(isAKnownPrime(n)||n==1)return n;
var q=[];while(q.length<=n)q.push(0);
while(n!=1){
for(var i=0;i<primes.length;i++){
var x=primes[i];
if(n%x==0){q[x]++;n/=x}
}
}
var o="";
for(var i=2;i<q.length;i++){
if(q[i]){if(o)o+="x";o+=i;if(q[i]>1){o+="^("+primeFactorize(q[i])+")"}}
}
return o;
}


You are required to make order of operations as clear as possible, and sort the prime factors in ascending order on each level.

You get a -50 byte bonus if you produce the output as formatted mathprint ORor valid latex code.

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain; and then output the result.

To make what I'm asking slightly clearer, here's a javascript program that does it, but, at 782 bytes, it's not very well golfed yet:

var primes=[2,3];
function nextPrime(){
var n=2;
while(isAMultipleOfAKnownPrime(n)){n++}
primes.push(n);
}
function isAKnownPrime(n){return primes.indexOf(n)!=-1};
function isAMultipleOfAKnownPrime(n){
for(var i=0;i<primes.length;i++)if(n%primes[i]==0)return true;
return false;
}
function primeFactorize(n){
while(primes[primes.length-1]<n)nextPrime();
if(isAKnownPrime(n)||n==1)return n;
var q=[];while(q.length<=n)q.push(0);
while(n!=1){
for(var i=0;i<primes.length;i++){
var x=primes[i];
if(n%x==0){q[x]++;n/=x}
}
}
var o="";
for(var i=2;i<q.length;i++){
if(q[i]){if(o)o+="x";o+=i;if(q[i]>1){o+="^("+primeFactorize(q[i])+")"}}
}
return o;
}


You are required to make order of operations as clear as possible, and sort the prime factors in ascending order on each level.

You get a -50 byte bonus if you produce the output as formatted mathprint OR latex code.

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain; and then output the result.

To make what I'm asking slightly clearer, here's a javascript program that does it, but, at 782 bytes, it's not very well golfed yet:

var primes=[2,3];
function nextPrime(){
var n=2;
while(isAMultipleOfAKnownPrime(n)){n++}
primes.push(n);
}
function isAKnownPrime(n){return primes.indexOf(n)!=-1};
function isAMultipleOfAKnownPrime(n){
for(var i=0;i<primes.length;i++)if(n%primes[i]==0)return true;
return false;
}
function primeFactorize(n){
while(primes[primes.length-1]<n)nextPrime();
if(isAKnownPrime(n)||n==1)return n;
var q=[];while(q.length<=n)q.push(0);
while(n!=1){
for(var i=0;i<primes.length;i++){
var x=primes[i];
if(n%x==0){q[x]++;n/=x}
}
}
var o="";
for(var i=2;i<q.length;i++){
if(q[i]){if(o)o+="x";o+=i;if(q[i]>1){o+="^("+primeFactorize(q[i])+")"}}
}
return o;
}


You are required to make order of operations as clear as possible, and sort the prime factors in ascending order on each level.

You get a -50 byte bonus if you produce the output as formatted mathprint or valid latex code.

2 added 14 characters in body

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain; and then output the result.

To make what I'm asking slightly clearer, here's a javascript program that does it, but, at 782 bytes, it's not very well golfed yet:

var primes=[2,3];
function nextPrime(){
var n=2;
while(isAMultipleOfAKnownPrime(n)){n++}
primes.push(n);
}
function isAKnownPrime(n){return primes.indexOf(n)!=-1};
function isAMultipleOfAKnownPrime(n){
for(var i=0;i<primes.length;i++)if(n%primes[i]==0)return true;
return false;
}
function primeFactorize(n){
while(primes[primes.length-1]<n)nextPrime();
if(isAKnownPrime(n)||n==1)return n;
var q=[];while(q.length<=n)q.push(0);
while(n!=1){
for(var i=0;i<primes.length;i++){
var x=primes[i];
if(n%x==0){q[x]++;n/=x}
}
}
var o="";
for(var i=2;i<q.length;i++){
if(q[i]){if(o)o+="x";o+=i;if(q[i]>1){o+="^("+primeFactorize(q[i])+")"}}
}
return o;
}


You are required to make order of operations as clear as possible, and sort the prime factors in ascending order on each level.

You get a -50 byte bonus if you produce the output as formatted mathprint OR latex code.

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain; and then output the result.

To make what I'm asking slightly clearer, here's a javascript program that does it, but, at 782 bytes, it's not very well golfed yet:

var primes=[2,3];
function nextPrime(){
var n=2;
while(isAMultipleOfAKnownPrime(n)){n++}
primes.push(n);
}
function isAKnownPrime(n){return primes.indexOf(n)!=-1};
function isAMultipleOfAKnownPrime(n){
for(var i=0;i<primes.length;i++)if(n%primes[i]==0)return true;
return false;
}
function primeFactorize(n){
while(primes[primes.length-1]<n)nextPrime();
if(isAKnownPrime(n)||n==1)return n;
var q=[];while(q.length<=n)q.push(0);
while(n!=1){
for(var i=0;i<primes.length;i++){
var x=primes[i];
if(n%x==0){q[x]++;n/=x}
}
}
var o="";
for(var i=2;i<q.length;i++){
if(q[i]){if(o)o+="x";o+=i;if(q[i]>1){o+="^("+primeFactorize(q[i])+")"}}
}
return o;
}


You are required to make order of operations as clear as possible, and sort the prime factors in ascending order on each level.

You get a -50 byte bonus if you produce the output as formatted mathprint.

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain; and then output the result.

To make what I'm asking slightly clearer, here's a javascript program that does it, but, at 782 bytes, it's not very well golfed yet:

var primes=[2,3];
function nextPrime(){
var n=2;
while(isAMultipleOfAKnownPrime(n)){n++}
primes.push(n);
}
function isAKnownPrime(n){return primes.indexOf(n)!=-1};
function isAMultipleOfAKnownPrime(n){
for(var i=0;i<primes.length;i++)if(n%primes[i]==0)return true;
return false;
}
function primeFactorize(n){
while(primes[primes.length-1]<n)nextPrime();
if(isAKnownPrime(n)||n==1)return n;
var q=[];while(q.length<=n)q.push(0);
while(n!=1){
for(var i=0;i<primes.length;i++){
var x=primes[i];
if(n%x==0){q[x]++;n/=x}
}
}
var o="";
for(var i=2;i<q.length;i++){
if(q[i]){if(o)o+="x";o+=i;if(q[i]>1){o+="^("+primeFactorize(q[i])+")"}}
}
return o;
}


You are required to make order of operations as clear as possible, and sort the prime factors in ascending order on each level.

You get a -50 byte bonus if you produce the output as formatted mathprint OR latex code.

1

# Recursive Prime Factorization

Your job is to take the prime factors of a number taken from input (omitting any exponents equal to 1) then take the prime factors of all of the exponents, and so on, until no composite numbers remain; and then output the result.

To make what I'm asking slightly clearer, here's a javascript program that does it, but, at 782 bytes, it's not very well golfed yet:

var primes=[2,3];
function nextPrime(){
var n=2;
while(isAMultipleOfAKnownPrime(n)){n++}
primes.push(n);
}
function isAKnownPrime(n){return primes.indexOf(n)!=-1};
function isAMultipleOfAKnownPrime(n){
for(var i=0;i<primes.length;i++)if(n%primes[i]==0)return true;
return false;
}
function primeFactorize(n){
while(primes[primes.length-1]<n)nextPrime();
if(isAKnownPrime(n)||n==1)return n;
var q=[];while(q.length<=n)q.push(0);
while(n!=1){
for(var i=0;i<primes.length;i++){
var x=primes[i];
if(n%x==0){q[x]++;n/=x}
}
}
var o="";
for(var i=2;i<q.length;i++){
if(q[i]){if(o)o+="x";o+=i;if(q[i]>1){o+="^("+primeFactorize(q[i])+")"}}
}
return o;
}