A316202 Number of integer partitions of n into Fermi-Dirac primes.

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

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