OFFSET
0,5
FORMULA
a(n) = A322900(n) - 1. - Gus Wiseman, Jan 01 2019
EXAMPLE
a(5)=1 since the only partition without 1 as a part is 5 (a power of 5). a(6)=4 since 6 can be written as 6 (powers of 6), 3+3 (powers of 3) and 4+2 and 2+2+2 (both powers of 2).
From Gus Wiseman, Jan 01 2019: (Start)
The a(2) = 1 through a(12) = 10 integer partitions (A = 10, B = 11, C = 12):
(2) (3) (4) (5) (6) (7) (8) (9) (A) (B) (C)
(22) (33) (44) (333) (55) (66)
(42) (422) (82) (84)
(222) (2222) (442) (93)
(4222) (444)
(22222) (822)
(3333)
(4422)
(42222)
(222222)
(End)
MATHEMATICA
radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All, 2]]);
Table[Length[Select[IntegerPartitions[n], And[FreeQ[#, 1], SameQ@@radbase/@#]&]], {n, 30}] (* Gus Wiseman, Jan 01 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jul 05 2002
STATUS
approved