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

0,8

Comments

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

Links

Table of n, a(n) for n=0..100.

Formula

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

Example

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

Mathematica

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

Crossrefs

Cf. A005117, A030229, A098235, A285797.

Sequence in context: A137347 A024941 A219492 * A317241 A361499 A287299

Adjacent sequences: A285793 A285794 A285795 * A285797 A285798 A285799

Keyword

nonn

Author

Ilya Gutkovskiy, Apr 26 2017

Status

approved