

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, 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
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

0,9


COMMENTS

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


LINKS

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


FORMULA

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


EXAMPLE

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


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]


CROSSREFS

Сf. A005117, A030059, A030229, A098235, A098236, A285796, A285797.
Sequence in context: A094718 A076191 A282318 * A025861 A090723 A027357
Adjacent sequences: A286968 A286969 A286970 * A286972 A286973 A286974


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, May 17 2017


STATUS

approved



