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 A287299 Number of ways of writing n as a sum of a proper prime power (A246547) and a nonprime squarefree number (A000469). 1
 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 2, 0, 0, 0, 2, 1, 0, 1, 2, 2, 0, 0, 2, 2, 1, 1, 3, 0, 1, 1, 4, 3, 0, 2, 2, 2, 0, 3, 4, 3, 1, 2, 6, 3, 1, 0, 5, 4, 2, 2, 4, 3, 0, 2, 3, 5, 0, 1, 3, 4, 3, 2, 4, 3, 3, 4, 5, 4, 0, 2, 5, 5, 0, 4, 6, 2, 1, 1, 7, 3, 1, 2, 7, 4, 2, 4, 5, 5, 1, 3, 6, 5, 1, 3, 6, 6, 3, 4, 4, 4, 2, 4, 7, 6, 3, 1, 4, 4, 0, 4, 6, 5, 2, 2, 7, 5, 2, 1, 7, 8, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,11 COMMENTS Conjecture: a(n) > 0 for all n > 108. LINKS Ilya Gutkovskiy, Extended graphical example Eric Weisstein's World of Mathematics, Prime Power Eric Weisstein's World of Mathematics, Squarefree FORMULA G.f.: (Sum_{k>=1} x^A246547(k))*(Sum_{k>=1} x^A000469(k)). EXAMPLE a(26) = 3 because we have [25, 1], [22, 4] and [16, 10]. MATHEMATICA nmax = 120; CoefficientList[Series[(Sum[Boole[SquareFreeQ[k] && ! PrimeQ[k]] x^k, {k, 1, nmax}]) (Sum[Boole[PrimePowerQ[k] && ! PrimeQ[k]] x^k, {k, 1, nmax}]), {x, 0, nmax}], x] PROG (PARI) x='x+O('x^120); concat([0, 0, 0, 0, 0], Vec(sum(k=1, 120, (issquarefree(k) && !isprime(k))*x^k) * sum(k=1, 120, (isprimepower(k) && !isprime(k))*x^k))) \\ Indranil Ghosh, May 23 2017 CROSSREFS Cf. A000469, A098983, A246547, A282192, A282290, A282318, A282947. Sequence in context: A219492 A285796 A317241 * A100699 A108921 A071548 Adjacent sequences: A287296 A287297 A287298 * A287300 A287301 A287302 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 23 2017 STATUS approved

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Last modified January 27 08:42 EST 2023. Contains 359838 sequences. (Running on oeis4.)