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 A195208 Number of odd divisors of !n. 2
 1, 0, 1, 1, 3, 2, 4, 6, 8, 8, 10, 4, 6, 12, 8, 4, 24, 4, 8, 24, 32, 16, 24, 96, 32, 48, 24, 16, 384, 32, 64, 144, 16, 8, 36, 128, 16, 80, 24, 16, 96, 32, 16, 96, 4, 16, 448, 128, 64, 24, 192, 48, 192, 64, 16, 96, 768, 32, 96, 32, 64 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS !k is a subfactorial number (A000166). LINKS EXAMPLE a(7) = 6 because the divisors of  !7 = 1854 are  {1, 2, 3, 6, 9, 18, 103, 206, 309, 618, 927, 1854} with 6  odd divisors  1, 3, 9, 103, 309 and 927 => 6 is in the sequence. MATHEMATICA f[n_] := Block[{d = Divisors[Subfactorial[n]]}, Count[OddQ[d], True]]; Table[f[n], {n, 0, 60}] PROG (PARI) a(n)=if(n<2, 1-n, my(x='x, k=n!*polcoeff(exp(-x+x*O(x^n))/(1-x), n)); numdiv(k>>valuation(k, 2))) \\ Charles R Greathouse IV, Sep 13 2011 CROSSREFS Cf. A000166, A195207. Sequence in context: A254052 A105746 A166309 * A114651 A240539 A138245 Adjacent sequences:  A195205 A195206 A195207 * A195209 A195210 A195211 KEYWORD nonn AUTHOR Michel Lagneau, Sep 13 2011 STATUS approved

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Last modified December 15 11:43 EST 2019. Contains 329999 sequences. (Running on oeis4.)