OFFSET
0,3
COMMENTS
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..10000
EXAMPLE
The a(5) = 6 integer partitions whose parts are 1's or not perfect powers are (5), (32), (311), (221), (2111), (11111).
MAPLE
q:= n-> is(n=1 or 1=igcd(map(i-> i[2], ifactors(n)[2])[])):
a:= proc(n) option remember; `if`(n=0, 1, add(a(n-j)*add(
`if`(q(d), d, 0), d=numtheory[divisors](j)), j=1..n)/n)
end:
seq(a(n), n=0..60); # Alois P. Heinz, Jun 07 2018
MATHEMATICA
nn=20;
radQ[n_]:=Or[n==1, GCD@@FactorInteger[n][[All, 2]]==1];
ser=Product[1/(1-x^p), {p, Select[Range[nn], radQ]}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, 0, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 07 2018
STATUS
approved