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 A321665 Number of strict integer partitions of n containing no 1's or prime powers. 5
 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 1, 1, 0, 2, 0, 2, 2, 2, 0, 3, 1, 3, 2, 4, 1, 5, 2, 5, 4, 6, 4, 9, 3, 8, 7, 10, 6, 13, 7, 13, 12, 16, 10, 20, 13, 22, 19, 24, 18, 32, 23, 34, 30, 37, 30, 49, 37, 50, 47, 58, 51, 73, 58, 77, 74, 89, 80, 108, 91, 116 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,19 LINKS Vaclav Kotesovec, Table of n, a(n) for n = 0..10000 (terms 0..500 from Fausto A. C. Cariboni) FORMULA G.f.: Product_{k>=2, k not a prime power} 1 + x^k. - Joerg Arndt, Dec 22 2020 EXAMPLE The a(36) = 9 strict integer partitions:   (36)   (30,6)   (21,15)   (22,14)   (24,12)   (26,10)   (18,12,6)   (20,10,6)   (14,12,10) MATHEMATICA nn=100; ser=Product[If[PrimePowerQ[n], 1, 1+x^n], {n, 2, nn}]; CoefficientList[Series[ser, {x, 0, nn}], x] CROSSREFS Cf. A000607, A000961, A001597, A002095, A023893, A023894, A096258, A246655, A321346, A321347, A321378, A322452, A322454. Sequence in context: A277486 A102395 A127504 * A329321 A334239 A335062 Adjacent sequences:  A321662 A321663 A321664 * A321666 A321667 A321668 KEYWORD nonn AUTHOR Gus Wiseman, Dec 11 2018 STATUS approved

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Last modified December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)