A195208 Number of odd divisors of !n.

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

Offset

0,5

Comments

!k is a subfactorial number (A000166).

Links

Table of n, a(n) for n=0..60.

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: A105746 A166309 A349472 * A114651 A340064 A240539

Adjacent sequences: A195205 A195206 A195207 * A195209 A195210 A195211

Keyword

nonn

Author

Michel Lagneau, Sep 13 2011

Status

approved