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 A336940 Number of odd divisors of n!. 2
 1, 1, 1, 2, 2, 4, 6, 12, 12, 20, 30, 60, 72, 144, 216, 336, 336, 672, 864, 1728, 2160, 3200, 4800, 9600, 10560, 14784, 22176, 28224, 35280, 70560, 86400, 172800, 172800, 245760, 368640, 497664, 559872, 1119744, 1679616, 2363904, 2626560, 5253120, 6451200, 12902400, 16128000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Seiichi Manyama, Table of n, a(n) for n = 0..10000 FORMULA a(n) = A001227(n!). a(n) = A000005(A049606(n)). a(n) + A337257(n) = A027423(n) = A000005(n!). From Seiichi Manyama, Aug 27 2020: (Start) If p is odd prime, a(p) = 2 * a(p-1). a(n) = A027423(n) / A113474(n) for n > 0. (End) EXAMPLE The a(1) = 1 through a(8) = 12 divisors:   1  1  1  1  1   1   1    1         3  3  3   3   3    3               5   5   5    5               15  9   7    7                   15  9    9                   45  15   15                       21   21                       35   35                       45   45                       63   63                       105  105                       315  315 MATHEMATICA Table[Length[Select[Divisors[n!], OddQ]], {n, 0, 15}] PROG (PARI) a(n) = sumdiv(n!, d, d%2); \\ Michel Marcus, Aug 24 2020 (PARI) a(n) = numdiv(prod(k=1, n, k >> valuation(k, 2))); \\ Michel Marcus, Aug 27 2020 CROSSREFS A049606 gives the maximum among these divisors, with quotient A060818. A337257 is the even version. A000265 gives the maximum odd divisor of n. A001227 counts odd divisors. A183063 counts even divisors. Cf. A000005, A001013, A001055, A006939, A113474, A124010, A253249. Factorial numbers: A000142, A022559, A027423 (divisors), A048656, A071626, A076716 (factorizations), A325272, A325273, A325617, A336414, A336498. Sequence in context: A318847 A228892 A267610 * A291365 A154779 A332983 Adjacent sequences:  A336937 A336938 A336939 * A336941 A336942 A336943 KEYWORD nonn AUTHOR Gus Wiseman, Aug 23 2020 EXTENSIONS a(36)-a(44) from Seiichi Manyama, Aug 26 2020 STATUS approved

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Last modified May 26 20:51 EDT 2022. Contains 354092 sequences. (Running on oeis4.)