A285796 Number of ways to write n as an ordered sum of two numbers that are the product of an even number of distinct primes (including 1).

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

Offset: 0

Author

Ilya Gutkovskiy, Apr 26 2017

Keywords

• nonn

Comments

Conjecture: a(n) > 0 for all n > 82.

Examples

			a(16) = 4 because we have [15, 1], [10, 6], [6, 10] and [1, 15].
		

Crossrefs

Cf. A005117, A030229, A098235, A285797.

Programs

Mathematica

nmax = 100; CoefficientList[Series[(Sum[Boole[MoebiusMu[k] == 1] x^k, {k, 1, nmax}])^2, {x, 0, nmax}], x]

Formula

G.f.: (Sum_{k>=1} x^A030229(k))^2.