A322912 Number of integer partitions of n whose parts are all powers of the same squarefree number.

1, 1, 2, 3, 5, 6, 10, 11, 15, 17, 23, 24, 33, 34, 42, 46, 56, 57, 71, 72, 88, 93, 109, 110, 134, 136, 158, 163, 191, 192, 229, 230, 266, 273, 311, 315, 370, 371, 419, 428, 491, 492, 565, 566, 642, 654, 730, 731, 836, 838, 936

Offset: 0

Author

Gus Wiseman, Dec 30 2018

Keywords

• nonn

Comments

First differs from A072720 at a(12) = 33, A072720(12) = 34.

Examples

			The a(1) = 1 through a(8) = 15 integer partitions:
  (1)  (2)   (3)    (4)     (5)      (6)       (7)        (8)
       (11)  (21)   (22)    (41)     (33)      (61)       (44)
             (111)  (31)    (221)    (42)      (331)      (71)
                    (211)   (311)    (51)      (421)      (422)
                    (1111)  (2111)   (222)     (511)      (611)
                            (11111)  (411)     (2221)     (2222)
                                     (2211)    (4111)     (3311)
                                     (3111)    (22111)    (4211)
                                     (21111)   (31111)    (5111)
                                     (111111)  (211111)   (22211)
                                               (1111111)  (41111)
                                                          (221111)
                                                          (311111)
                                                          (2111111)
                                                          (11111111)
		

Crossrefs

Cf. A000961, A005117, A018819, A023893, A052410, A072720, A072721, A072774, A302593, A322847, A322900, A322901, A322911.

Programs

Mathematica

radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All,2]]);
powsqfQ[n_]:=SameQ@@Last/@FactorInteger[n];
Table[Length[Select[IntegerPartitions[n],And[And@@powsqfQ/@#,SameQ@@radbase/@DeleteCases[#,1]]&]],{n,30}]