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.

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

Offset

0,5

Comments

The positions of zeros appear to be A048278.

Links

Table of n, a(n) for n=0..65.

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