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A374671
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Positive numbers k such that k! and (k+1)! have an equal number of infinitary divisors.
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4
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8, 19, 23, 44, 45, 57, 67, 76, 80, 83, 84, 85, 105, 107, 116, 120, 123, 140, 141, 146, 158, 161, 165, 174, 177, 187, 201, 208, 214, 225, 235, 239, 241, 243, 244, 246, 247, 263, 269, 272, 277, 284, 297, 309, 315, 321, 322, 325, 337, 339, 341, 342, 344, 360, 363
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OFFSET
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1,1
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COMMENTS
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Positive numbers such that k! and (k+1)! have an equal number of Fermi-Dirac factors (A064547).
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LINKS
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EXAMPLE
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MATHEMATICA
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s[n_] := s[n] = Module[{e = FactorInteger[n!][[;; , 2]]}, Sum[DigitCount[e[[k]], 2, 1], {k, 1, Length[e]}]]; Select[Range[2, 400], s[#] == s[# + 1] &]
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PROG
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(PARI) s(n) = {my(e = factor(n!)[, 2]); sum(k=1, #e, hammingweight(e[k])); }
lista(kmax) = {my(s1 = s(1), s2); for(k = 2, kmax, s2 = s(k); if(s1 == s2, print1(k-1, ", ")); s1 = s2); }
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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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