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A316211
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Number of strict integer partitions of n into Fermi-Dirac primes.
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3
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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
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OFFSET
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0,6
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COMMENTS
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A Fermi-Dirac prime (A050376) is a number of the form p^(2^k) where p is prime and k >= 0.
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LINKS
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FORMULA
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O.g.f.: Product_d (1 + x^d) where the product is over all Fermi-Dirac primes (A050376).
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EXAMPLE
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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).
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A000586, A000607, A050376, A064547, A213925, A279065, A299755, A299757, A305829, A316202, A316210, A316220.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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