A316211 Number of strict integer partitions of n into Fermi-Dirac primes.

1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 2, 4, 4, 4, 6, 4, 9, 5, 10, 8, 11, 11, 12, 15, 13, 19, 16, 21, 21, 24, 26, 27, 32, 31, 37, 37, 42, 44, 47, 52, 53, 61, 61, 69, 71, 78, 82, 88, 95, 99, 108, 112, 122, 128, 137, 144, 154, 163, 172, 184, 193, 206, 216, 230, 242, 256

Offset

0,6

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..65.

Formula

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

Example

The a(16) = 9 strict integer partitions of 16 into Fermi-Dirac primes:
(16),
(9,7), (11,5), (13,3),
(7,5,4), (9,4,3), (9,5,2), (11,3,2),
(7,4,3,2).

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+x^d, {d, FDprimeList}];
Table[SeriesCoefficient[ser, {x, 0, n}], {n, 0, nn}]

Crossrefs

Cf. A000586, A000607, A050376, A064547, A213925, A279065, A299755, A299757, A305829, A316202, A316210, A316220.

Sequence in context: A117172 A029207 A111902 * A329480 A277895 A328772

Adjacent sequences: A316208 A316209 A316210 * A316212 A316213 A316214

Keyword

nonn

Author

Gus Wiseman, Jun 26 2018

Status

approved