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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 * A287299 A100699 A108921

Adjacent sequences:  A285793 A285794 A285795 * A285797 A285798 A285799

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Apr 26 2017

STATUS

approved

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Last modified February 24 07:50 EST 2018. Contains 299599 sequences. (Running on oeis4.)