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

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, 24, 26, 27, 32, 31, 37, 37, 42, 44, 47, 52, 53, 61, 61, 69, 71, 78, 82, 88, 95, 99, 108, 112, 122, 128, 137, 144, 154, 163, 172, 184, 193, 206, 216, 230, 242, 256

Offset: 0

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(16) = 9 strict integer partitions of 16 into Fermi-Dirac primes:
(16),
(9,7), (11,5), (13,3),
(7,5,4), (9,4,3), (9,5,2), (11,3,2),
(7,4,3,2).
		

Crossrefs

Cf. A000586, A000607, A050376, A064547, A213925, A279065, A299755, A299757, A305829, A316202, A316210, 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+x^d,{d,FDprimeList}];
Table[SeriesCoefficient[ser,{x,0,n}],{n,0,nn}]

Formula

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