cp's OEIS Frontend

A316211 Number of strict integer partitions of n into Fermi-Dirac primes.

%I A316211 #7 Jun 27 2018 07:07:41
%S A316211 1,0,1,1,1,2,1,3,1,4,2,4,4,4,6,4,9,5,10,8,11,11,12,15,13,19,16,21,21,
%T A316211 24,26,27,32,31,37,37,42,44,47,52,53,61,61,69,71,78,82,88,95,99,108,
%U A316211 112,122,128,137,144,154,163,172,184,193,206,216,230,242,256
%N A316211 Number of strict integer partitions of n into Fermi-Dirac primes.
%C A316211 A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0.
%F A316211 O.g.f.: Product_d (1 + x^d) where the product is over all Fermi-Dirac primes (A050376).
%e A316211 The a(16) = 9 strict integer partitions of 16 into Fermi-Dirac primes:
%e A316211 (16),
%e A316211 (9,7), (11,5), (13,3),
%e A316211 (7,5,4), (9,4,3), (9,5,2), (11,3,2),
%e A316211 (7,4,3,2).
%t A316211 nn=60;
%t A316211 FDpQ[n_]:=With[{f=FactorInteger[n]},n>1&&Length[f]==1&&MatchQ[FactorInteger[2f[[1,2]]],{{2,_}}]]
%t A316211 FDprimeList=Select[Range[nn],FDpQ];
%t A316211 ser=Product[1+x^d,{d,FDprimeList}];
%t A316211 Table[SeriesCoefficient[ser,{x,0,n}],{n,0,nn}]
%Y A316211 Cf. A000586, A000607, A050376, A064547, A213925, A279065, A299755, A299757, A305829, A316202, A316210, A316220.
%K A316211 nonn
%O A316211 0,6
%A A316211 _Gus Wiseman_, Jun 26 2018