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

0,3

Comments

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

Links

Table of n, a(n) for n=0..50.

Example

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)

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}]

Crossrefs

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

Sequence in context: A057760 A074243 A302539 * A072720 A325354 A298363

Adjacent sequences: A322909 A322910 A322911 * A322913 A322914 A322915

Keyword

nonn

Author

Gus Wiseman, Dec 30 2018

Status

approved