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If – as usual – σ₀(k) denotes the number of positive divisors of the integer k, we can define a_n is the smallest positive integer such that 2σ₀((a_n - n) / 3) = f_n+1 - f_n.

If we remove every second element of the natural numbers, we are left with

These are the terms F₁ to F₇.

If – as usual – σ₀(k) denotes the number of positive divisors of the integer k, we can define a_n as the smallest positive integer such that 2σ₀((a_n - n) / 3) = f_n+1 - f_n.

If we remove every second element of the positive integers, we are left with

The last row shows the terms f₁ to f₇.

a_n is the smallest positive integer such that a_n - n is an entire multiple of 3 and twice the number of divisors of (a_n - n) / 3 gives the n^th term in the first differences of the sequence produced by the Flavius-Josephus sieve.

The Flavius Josephus's sieve defines an integer sequence as follows.

a_n is the smallest positive integer such that a_n - n is an entire multiple of 3 and twice the number of divisors of (a_n - n) / 3 gives the n^th term in the first differences of the sequence produced by the Flavius Josephus sieve.

The Flavius Josephus sieve defines an integer sequence as follows.

The Flavius Josephus's sieve defines an integer sequence as follows.

The Flavius Josephus's sieve defines an integer sequence as follows.