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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
OFFSET
0,8
COMMENTS
Conjecture: a(n) > 0 for all n > 82.
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
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Apr 26 2017
STATUS
approved