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 A286305 Number of partitions of n into powerful parts (A001694). 1
 1, 1, 1, 1, 2, 2, 2, 2, 4, 5, 5, 5, 7, 8, 8, 8, 12, 14, 15, 15, 19, 21, 22, 22, 28, 33, 35, 37, 43, 48, 50, 52, 62, 70, 75, 79, 92, 100, 105, 109, 126, 140, 148, 157, 177, 194, 202, 211, 237, 261, 276, 290, 324, 351, 370, 384, 424, 462, 489, 514, 562, 609, 640, 670, 728, 787, 831, 873, 948, 1016, 1071, 1118, 1210, 1296, 1366, 1433 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Eric Weisstein's World of Mathematics, Powerful Number FORMULA G.f.: Product_{k>=1} 1/(1 - x^A001694(k)). a(n) = A078635(n) for n < 72. EXAMPLE a(8) = 4 because we have [8], [4, 4], [4, 1, 1, 1, 1] and [1, 1, 1, 1, 1, 1, 1, 1]. MATHEMATICA nmax = 75; CoefficientList[Series[1/(1 - x) Product[1/(1 - Boole[Min@ FactorInteger[k][[All, 2]] > 1] x^k), {k, 2, nmax}], {x, 0, nmax}], x] CROSSREFS Cf. A001694, A078635, A286320. Sequence in context: A029078 A131799 A078635 * A046768 A274151 A216393 Adjacent sequences:  A286302 A286303 A286304 * A286306 A286307 A286308 KEYWORD nonn AUTHOR Ilya Gutkovskiy, May 12 2017 STATUS approved

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Last modified May 8 11:30 EDT 2021. Contains 343666 sequences. (Running on oeis4.)