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

1,3

Comments

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

Links

Table of n, a(n) for n=1..41.

Example

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

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]}]

Crossrefs

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

Sequence in context: A094686 A277752 A095054 * A032162 A000983 A095325

Adjacent sequences: A316207 A316208 A316209 * A316211 A316212 A316213

Keyword

nonn

Author

Gus Wiseman, Jun 26 2018

Status

approved