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

0,5

Comments

!n is a subfactorial number (A000166).

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

Links

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

Formula

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A004454 A113548 A249998 * A175850 A176306 A291368

Adjacent sequences: A195207 A195208 A195209 * A195211 A195212 A195213

Keyword

nonn

Author

Michel Lagneau, Sep 13 2011

Extensions

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

Status

approved