A320322 Number of integer partitions of n whose product is a perfect power.

1, 0, 0, 0, 2, 2, 5, 5, 9, 11, 18, 19, 28, 30, 42, 50, 68, 76, 102, 113, 146, 170, 212, 241, 312, 356, 441, 514, 628, 720, 887, 1008, 1215, 1403, 1660, 1903, 2291, 2609, 3107, 3594, 4254, 4864, 5739, 6546, 7672, 8811, 10237, 11651, 13583, 15420, 17867, 20382

Offset

0,5

Links

Table of n, a(n) for n=0..51.

Example

The a(4) = 2 through a(11) = 19 integer partitions:
  4   41   33    331    8       9        55        551
  22  221  42    421    44      81       82        632
           222   2221   422     333      91        821
           411   4111   2222    441      433       911
           2211  22111  3311    4221     442       4331
                        4211    22221    811       4421
                        22211   33111    3322      8111
                        41111   42111    3331      33221
                        221111  222111   4222      33311
                                411111   4411      42221
                                2211111  22222     44111
                                         42211     222221
                                         222211    422111
                                         331111    2222111
                                         421111    3311111
                                         2221111   4211111
                                         4111111   22211111
                                         22111111  41111111
                                                   221111111

Mathematica

Table[Length[Select[IntegerPartitions[n], GCD@@FactorInteger[Times@@#][[All, 2]]>1&]], {n, 30}]

Crossrefs

Cf. A003963, A064573, A305551, A319056, A319066, A319071, A319169, A320325.

Sequence in context: A071181 A213675 A321185 * A330106 A214795 A287744

Adjacent sequences: A320319 A320320 A320321 * A320323 A320324 A320325

Keyword

nonn

Author

Gus Wiseman, Oct 10 2018

Status

approved