

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).


2



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



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

Сf. A005117, A030229, A098235, A285797.
Sequence in context: A137347 A024941 A219492 * A317241 A287299 A100699
Adjacent sequences: A285793 A285794 A285795 * A285797 A285798 A285799


KEYWORD

nonn


AUTHOR

Ilya Gutkovskiy, Apr 26 2017


STATUS

approved



