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A316202 Number of integer partitions of n into Fermi-Dirac primes. 4
1, 0, 1, 1, 2, 2, 3, 4, 5, 7, 8, 11, 13, 17, 20, 25, 31, 37, 45, 54, 65, 77, 92, 109, 128, 152, 177, 208, 242, 283, 327, 380, 439, 506, 583, 669, 768, 878, 1004, 1144, 1303, 1482, 1681, 1906, 2156, 2438, 2750, 3101, 3490, 3924, 4407, 4942, 5538, 6197, 6929 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,5

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=0..54.

FORMULA

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

EXAMPLE

The a(12) = 13 integer partitions of 12 into Fermi-Dirac primes:

(75), (93),

(444), (543), (552), (732),

(3333), (4332), (4422), (5322),

(33222), (42222),

(222222).

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, n}], {n, 0, nn}]

CROSSREFS

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

Sequence in context: A017841 A304329 A111901 * A326671 A134727 A152305

Adjacent sequences:  A316199 A316200 A316201 * A316203 A316204 A316205

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 26 2018

STATUS

approved

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Last modified July 4 09:40 EDT 2020. Contains 335446 sequences. (Running on oeis4.)