cp's OEIS Frontend

From Jon E. Schoenfield, Apr 30 2022: (Start)

This sequence includes all noncomposite numbers, the squares of all odd primes, and the cube of every odd prime p such that p^3 - 2 is composite.

It also includes every number k of the form p*q, with p and q distinct primes, such that k-2 is composite and k-1 is neither a prime nor the square of a prime.

In general, it includes every number k such that tau(k-j) > tau(k) - j for each j in 1..tau(k)-1.

Terms with larger numbers of divisors occur less frequently. The first terms with 0, 1, 2, 3, and 4 distinct prime factors are 1, 3, 22, 2110, and 17585778, respectively (each of which is squarefree). What is the first term with 5 distinct prime factors?

(End)

a(n) = SG(2*n) where SG(n) = mex{x in opt(n)} SG(x), where mex(A) is the least nonnegative integer not appearing in A, and opt(n) is a vector of values n-k where 1 <= k <= n is not a divisor of n. For odd n, SG(n) = (n-1)/2.

Note that SG(n) represents the nim-value (also called the Sprague-Grundy number) for position n in combinatorial game theory. It indicates the winning strategy for that position when both players play optimally.