OFFSET
0,3
FORMULA
a(n) = a(n-1) + A072721(n). a(p) = a(p-1)+1 for p prime.
EXAMPLE
a(6)=10 since 6 can be written as 6 (powers of 6), 5+1 (5), 4+1+1 (4 or 2), 3+3 (3), 3+1+1+1 (3), 4+2 (2), 2+2+2 (2), 2+2+1+1 (2), 2+1+1+1+1 (2) and 1+1+1+1+1+1 (powers of anything).
From Gus Wiseman, Jan 01 2019: (Start)
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)
(End)
MATHEMATICA
radbase[n_]:=n^(1/GCD@@FactorInteger[n][[All, 2]]);
Table[Length[Select[IntegerPartitions[n], SameQ@@radbase/@DeleteCases[#, 1]&]], {n, 30}] (* Gus Wiseman, Jan 01 2019 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Henry Bottomley, Jul 05 2002
STATUS
approved