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A319827
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FDH numbers of relatively prime strict integer partitions.
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3
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2, 6, 8, 10, 12, 14, 18, 20, 21, 22, 24, 26, 28, 30, 32, 33, 34, 35, 38, 40, 42, 44, 46, 48, 50, 52, 54, 55, 56, 57, 58, 60, 62, 63, 66, 68, 70, 72, 74, 75, 76, 77, 78, 80, 82, 84, 86, 88, 90, 91, 93, 94, 95, 96, 98, 99, 100, 102, 104, 105, 106, 108, 110, 112
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OFFSET
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1,1
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COMMENTS
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Let f(n) = A050376(n) be the n-th Fermi-Dirac prime. The FDH number of a strict integer partition (y_1, ..., y_k) is f(y_1) * ... * f(y_k).
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LINKS
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EXAMPLE
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The sequence of all relatively prime strict integer partitions begins: (1), (2,1), (3,1), (4,1), (3,2), (5,1), (6,1), (4,3), (5,2), (7,1), (3,2,1), (8,1), (5,3), (4,2,1).
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MATHEMATICA
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nn=200;
FDfactor[n_]:=If[n==1, {}, Sort[Join@@Cases[FactorInteger[n], {p_, k_}:>Power[p, Cases[Position[IntegerDigits[k, 2]//Reverse, 1], {m_}:>2^(m-1)]]]]];
FDprimeList=Array[FDfactor, nn, 1, Union]; FDrules=MapIndexed[(#1->#2[[1]])&, FDprimeList];
Select[Range[nn], GCD@@(FDfactor[#]/.FDrules)==1&]
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CROSSREFS
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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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