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A374672
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Numbers k such that k! has more infinitary divisors than (k+1)!.
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4
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5, 9, 17, 27, 33, 34, 35, 43, 48, 51, 53, 59, 65, 68, 69, 75, 77, 87, 91, 97, 98, 99, 103, 115, 119, 125, 129, 134, 135, 139, 147, 149, 151, 155, 163, 164, 171, 179, 183, 189, 194, 195, 197, 199, 203, 211, 215, 221, 227, 229, 230, 231, 237, 245, 249, 257, 259
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OFFSET
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1,1
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COMMENTS
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Numbers k such that k! has more Fermi-Dirac factors (A064547) than (k+1)!.
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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, 300], 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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