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A322912 Number of integer partitions of n whose parts are all powers of the same squarefree number. 3
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 (list; graph; refs; listen; history; text; internal format)
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 A298363 A018396

Adjacent sequences:  A322909 A322910 A322911 * A322913 A322914 A322915

KEYWORD

nonn

AUTHOR

Gus Wiseman, Dec 30 2018

STATUS

approved

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Last modified February 19 18:22 EST 2019. Contains 320327 sequences. (Running on oeis4.)