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 A322900 Number of integer partitions of n whose parts are all proper powers of the same number. 7
 1, 1, 2, 2, 3, 2, 5, 2, 5, 3, 7, 2, 11, 2, 9, 5, 11, 2, 16, 2, 18, 6, 17, 2, 27, 3, 23, 6, 30, 2, 38, 2, 37, 8, 39, 5, 58, 2, 49, 10, 66, 2, 74, 2, 78, 14, 77, 2, 109, 3, 100, 12, 118, 2, 131, 6, 146, 15, 143, 2, 190, 2, 169, 20, 203, 6, 224, 2, 242, 18, 248 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Such a partition contains either no 1's or only 1's. A proper power of n is a number n^k for some positive integer k. Also integer partitions whose parts all have the same radical base (A052410). LINKS EXAMPLE The a(1) = 1 through a(14) = 9 integer partitions (A = 10, B = 11, C = 12, D = 13, E = 14):   (1) (2)  (3)   (4)    (5)     (6)      (7)       (8)        (9)       (11) (111) (22)   (11111) (33)     (1111111) (44)       (333)                  (1111)         (42)               (422)      (111111111)                                 (222)              (2222)                                 (111111)           (11111111) .   (A)          (B)           (C)            (D)             (E)   (55)         (11111111111) (66)           (1111111111111) (77)   (82)                       (84)                           (842)   (442)                      (93)                           (4442)   (4222)                     (444)                          (8222)   (22222)                    (822)                          (44222)   (1111111111)               (3333)                         (422222)                              (4422)                         (2222222)                              (42222)                        (11111111111111)                              (222222)                              (111111111111) MATHEMATICA radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All, 2]]); Table[Length[Select[IntegerPartitions[n], SameQ@@radbase/@#&]], {n, 30}] CROSSREFS a(n) = A072721(n) + 1. Cf. A000961, A001597, A018819, A023893, A023894, A052409, A052410, A072720, A102430, A302593, A322901, A322902, A322903. Sequence in context: A180125 A272209 A323347 * A238791 A007012 A298423 Adjacent sequences:  A322897 A322898 A322899 * A322901 A322902 A322903 KEYWORD nonn AUTHOR Gus Wiseman, Dec 30 2018 STATUS approved

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Last modified April 18 12:34 EDT 2019. Contains 322209 sequences. (Running on oeis4.)