A316210 - OEIS

%I #7 Jun 27 2018 07:07:34

%S 1,1,2,2,4,7,11,17,31,37,54,109,152,283,380,878,1482,1906,3101,3924,

%T 6197,11915,14703,27063,40016,48450,84633,101419,121250,204461,398916,

%U 551093,646073,883626,1030952,1397083,2522506,3875455,5128718,7741307,8860676

%N Number of integer partitions of the n-th Fermi-Dirac prime into Fermi-Dirac primes.

%C A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0.

%e The a(6) = 7 partitions of 9 into Fermi-Dirac primes are (9), (54), (72), (333), (432), (522), (3222).

%t nn=60;

%t FDpQ[n_]:=With[{f=FactorInteger[n]},n>1&&Length[f]==1&&MatchQ[FactorInteger[2f[[1,2]]],{{2,_}}]]

%t FDprimeList=Select[Range[nn],FDpQ];

%t ser=Product[1/(1-x^d),{d,FDprimeList}];

%t Table[SeriesCoefficient[ser,{x,0,FDprimeList[[n]]}],{n,Length[FDprimeList]}]

%Y Cf. A000586, A000607, A050376, A064547, A213925, A279065, A299755, A299757, A305829, A316202, A316211, A316220.

%K nonn

%O 1,3

%A _Gus Wiseman_, Jun 26 2018