A195210 Sum of odd divisors of !n.

1, 0, 1, 1, 13, 12, 324, 1352, 18368, 19152, 1994322, 8810748, 193690826, 829046868, 34563283272, 274895151856, 14554448767872, 8178592487376, 2493850026398472, 33842416675133248, 1037660717168380800, 6072370562498569056, 682597834324732589120, 5390950170768906240000

Offset: 0

Author

Michel Lagneau, Sep 13 2011

Keywords

• nonn

Comments

!n is a subfactorial number (A000166).

Property of the sequence: for n > 4 the sum of odd divisors of !n seems even.

Examples

			a(7) = 1352 because the divisors of  !7 = 1854 are  {1, 2, 3, 6, 9, 18, 103, 206, 309, 618, 927, 1854}, and the sum of the 6  odd divisors  1, 3, 9, 103, 309 and 927 is 1352.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..81

Crossrefs

Cf. A000166, A000593, A195207, A195208, A195209.

Programs

Mathematica

Table[Total[Select[Divisors[Subfactorial[n]], OddQ[ # ]&]], {n, 0, 21}]

Formula

a(n) = A000593(A000166(n)), for n != 1. - Amiram Eldar, Aug 02 2024

Extensions

a(22)-a(23) from Amiram Eldar, Aug 02 2024