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).
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
KEYWORD
nonn
AUTHOR
Gus Wiseman, Dec 30 2018
STATUS
approved