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 A299200 Number of twice-partitions whose domain is the integer partition with Heinz number n. 10
 1, 1, 2, 1, 3, 2, 5, 1, 4, 3, 7, 2, 11, 5, 6, 1, 15, 4, 22, 3, 10, 7, 30, 2, 9, 11, 8, 5, 42, 6, 56, 1, 14, 15, 15, 4, 77, 22, 22, 3, 101, 10, 135, 7, 12, 30, 176, 2, 25, 9, 30, 11, 231, 8, 21, 5, 44, 42, 297, 6, 385, 56, 20, 1, 33, 14, 490, 15, 60, 15, 627, 4 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS The Heinz number of an integer partition (y_1,...,y_k) is prime(y_1)*...*prime(y_k). LINKS FORMULA Multiplicative with a(prime(n)) = A000041(n). EXAMPLE The a(15) = 6 twice-partitions: (3)(2), (3)(11), (21)(2), (21)(11), (111)(2), (111)(11). MATHEMATICA Table[Times@@Cases[FactorInteger[n], {p_, k_}:>PartitionsP[PrimePi[p]]^k], {n, 100}] PROG (PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = numbpart(primepi(f[k, 1])); ); factorback(f); } \\ Michel Marcus, Feb 26 2018 CROSSREFS Cf. A000041, A063834, A112798, A196545, A273873, A281145, A289501, A290261, A296150, A299201, A299202, A299203. Sequence in context: A064989 A290099 A250479 * A321272 A321270 A030067 Adjacent sequences:  A299197 A299198 A299199 * A299201 A299202 A299203 KEYWORD nonn,mult AUTHOR Gus Wiseman, Feb 05 2018 STATUS approved

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Last modified December 5 13:26 EST 2019. Contains 329751 sequences. (Running on oeis4.)