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A316211 Number of strict integer partitions of n into Fermi-Dirac primes. 3


%S 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 24,26,27,32,31,37,37,42,44,47,52,53,61,61,69,71,78,82,88,95,99,108,

%U 112,122,128,137,144,154,163,172,184,193,206,216,230,242,256

%N Number of strict integer partitions of n 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.

%F O.g.f.: Product_d (1 + x^d) where the product is over all Fermi-Dirac primes (A050376).

%e The a(16) = 9 strict integer partitions of 16 into Fermi-Dirac primes:

%e (16),

%e (9,7), (11,5), (13,3),

%e (7,5,4), (9,4,3), (9,5,2), (11,3,2),

%e (7,4,3,2).

%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+x^d,{d,FDprimeList}];

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

%Y Cf. A000586, A000607, A050376, A064547, A213925, A279065, A299755, A299757, A305829, A316202, A316210, A316220.

%K nonn

%O 0,6

%A _Gus Wiseman_, Jun 26 2018

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Last modified July 9 16:24 EDT 2020. Contains 335544 sequences. (Running on oeis4.)