cp's OEIS Frontend

A316202 Number of integer partitions of n into Fermi-Dirac primes.

%I A316202 #6 Jun 27 2018 07:07:26
%S A316202 1,0,1,1,2,2,3,4,5,7,8,11,13,17,20,25,31,37,45,54,65,77,92,109,128,
%T A316202 152,177,208,242,283,327,380,439,506,583,669,768,878,1004,1144,1303,
%U A316202 1482,1681,1906,2156,2438,2750,3101,3490,3924,4407,4942,5538,6197,6929
%N A316202 Number of integer partitions of n into Fermi-Dirac primes.
%C A316202 A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0.
%F A316202 O.g.f.: Product_d 1/(1 - x^d) where the product is over all Fermi-Dirac primes (A050376).
%e A316202 The a(12) = 13 integer partitions of 12 into Fermi-Dirac primes:
%e A316202 (75), (93),
%e A316202 (444), (543), (552), (732),
%e A316202 (3333), (4332), (4422), (5322),
%e A316202 (33222), (42222),
%e A316202 (222222).
%t A316202 nn=60;
%t A316202 FDpQ[n_]:=With[{f=FactorInteger[n]},n>1&&Length[f]==1&&MatchQ[FactorInteger[2f[[1,2]]],{{2,_}}]]
%t A316202 FDprimeList=Select[Range[nn],FDpQ];
%t A316202 ser=Product[1/(1-x^d),{d,FDprimeList}];
%t A316202 Table[SeriesCoefficient[ser,{x,0,n}],{n,0,nn}]
%Y A316202 Cf. A000586, A000607, A050376, A064547, A213925, A279065, A299755, A299757, A305829.
%K A316202 nonn
%O A316202 0,5
%A A316202 _Gus Wiseman_, Jun 26 2018