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A316210 Number of integer partitions of the n-th Fermi-Dirac prime into Fermi-Dirac primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 27 21:52 EDT 2020. Contains 334671 sequences. (Running on oeis4.)