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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
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.
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}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jun 26 2018
STATUS
approved