A316210 Number of integer partitions of the n-th Fermi-Dirac prime into Fermi-Dirac primes.

1, 1, 2, 2, 4, 7, 11, 17, 31, 37, 54, 109, 152, 283, 380, 878, 1482, 1906, 3101, 3924, 6197, 11915, 14703, 27063, 40016, 48450, 84633, 101419, 121250, 204461, 398916, 551093, 646073, 883626, 1030952, 1397083, 2522506, 3875455, 5128718, 7741307, 8860676

Offset: 1

Author

Gus Wiseman, Jun 26 2018

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

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

Programs

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/(1-x^d),{d,FDprimeList}];
Table[SeriesCoefficient[ser,{x,0,FDprimeList[[n]]}],{n,Length[FDprimeList]}]