OFFSET
0,5
COMMENTS
A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0.
FORMULA
O.g.f.: Product_d 1/(1 - x^d) where the product is over all Fermi-Dirac primes (A050376).
EXAMPLE
The a(12) = 13 integer partitions of 12 into Fermi-Dirac primes:
(75), (93),
(444), (543), (552), (732),
(3333), (4332), (4422), (5322),
(33222), (42222),
(222222).
MATHEMATICA
nn=60;
FDpQ[n_]:=With[{f=FactorInteger[n]}, n>1&&Length[f]==1&&MatchQ[FactorInteger[2f[[1, 2]]], {{2, _}}]]
FDprimeList=Select[Range[nn], FDpQ];
ser=Product[1/(1-x^d), {d, FDprimeList}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, 0, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 26 2018
STATUS
approved