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A316211 Number of strict integer partitions of n into Fermi-Dirac primes. 3
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 (list; graph; refs; listen; history; text; internal format)
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 * A277895 A328772 A300726

Adjacent sequences:  A316208 A316209 A316210 * A316212 A316213 A316214

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jun 26 2018

STATUS

approved

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Last modified June 6 18:59 EDT 2020. Contains 334832 sequences. (Running on oeis4.)