OFFSET
0,6
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 + x^d) where the product is over all Fermi-Dirac primes (A050376).
EXAMPLE
The a(16) = 9 strict integer partitions of 16 into Fermi-Dirac primes:
(16),
(9,7), (11,5), (13,3),
(7,5,4), (9,4,3), (9,5,2), (11,3,2),
(7,4,3,2).
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+x^d, {d, FDprimeList}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, 0, nn}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 26 2018
STATUS
approved