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 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 Cf. A005117, A030059, A030229, A098235, A098236, A285796, A285797. Sequence in context: A076191 A362955 A282318 * A025861 A090723 A027357 Adjacent sequences: A286968 A286969 A286970 * A286972 A286973 A286974 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 17 2017 STATUS approved

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Last modified August 6 22:32 EDT 2024. Contains 374998 sequences. (Running on oeis4.)