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 A319071 Number of integer partitions of n whose product of parts is a perfect power and whose parts all have the same number of prime factors, counted with multiplicity. 4
 1, 0, 0, 0, 2, 0, 2, 0, 3, 2, 3, 0, 4, 1, 4, 3, 7, 1, 7, 1, 8, 6, 8, 0, 15, 5, 12, 6, 15, 4, 22, 4, 24, 12, 22, 8, 35, 7, 30, 16, 42, 9, 50, 9, 50, 30, 53, 7, 79, 22, 72, 33, 87, 21, 109, 26, 111, 55, 117, 24, 168, 40, 149, 65, 178, 59 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS The positions of zeros appear to be A048278. LINKS EXAMPLE The a(4) = 2 through a(16) = 7 integer partitions (G = 16):   4   33   8     9    55     66      94  77       555     G   22  222  44    333  3322   444         5522     33333   88            2222       22222  3333        332222   333222  664                              222222      2222222          4444                                                           5533                                                           333322                                                           22222222 MATHEMATICA Table[Length[Select[IntegerPartitions[n], And[GCD@@FactorInteger[Times@@#][[All, 2]]>1, SameQ@@PrimeOmega/@#]&]], {n, 30}] CROSSREFS Cf. A003963, A048278, A064573, A279787, A305551, A319056, A319066, A319169, A320322, A320323. Sequence in context: A144494 A136166 A259525 * A316432 A046522 A242896 Adjacent sequences:  A319068 A319069 A319070 * A319072 A319073 A319074 KEYWORD nonn AUTHOR Gus Wiseman, Oct 10 2018 STATUS approved

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Last modified June 17 00:17 EDT 2021. Contains 345080 sequences. (Running on oeis4.)