A286971 Number of ways to write n as a sum of two numbers, one of which is the product of an even number of distinct primes (including 1) (A030229) and another is the product of an odd number of distinct primes (A030059).

0, 0, 0, 1, 1, 0, 1, 0, 2, 1, 0, 1, 2, 2, 1, 1, 1, 4, 2, 2, 2, 2, 1, 3, 3, 3, 2, 3, 3, 4, 1, 3, 3, 4, 2, 3, 3, 5, 5, 4, 5, 5, 3, 5, 6, 6, 4, 3, 4, 4, 3, 7, 7, 6, 3, 3, 6, 8, 6, 4, 4, 3, 8, 8, 8, 7, 2, 7, 10, 8, 5, 5, 6, 4, 8, 8, 12, 7, 3, 7, 11, 11, 8, 3, 7, 9, 6, 10, 14, 8, 4, 5, 12, 13, 10, 7, 9, 8, 12, 13, 12

Offset: 0

Author

Ilya Gutkovskiy, May 17 2017

Keywords

• nonn

Comments

Conjecture: a(n) > 0 for all n > 10.

Examples

			a(17) = 4 because we have [15, 2], [14, 3], [11, 6] and [10, 7].
		

Crossrefs

Cf. A005117, A030059, A030229, A098235, A098236, A285796, A285797.

Programs

Mathematica

nmax = 100; CoefficientList[Series[(Sum[Boole[MoebiusMu[k] == 1] x^k, {k, 1, nmax}]) (Sum[Boole[MoebiusMu[k] == -1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]

Formula

G.f.: (Sum_{i>=1} x^A030229(i))*(Sum_{j>=1} x^A030059(j)).