A193337 Sum of odd divisors of sigma(n).

1, 4, 1, 8, 4, 4, 1, 24, 14, 13, 4, 8, 8, 4, 4, 32, 13, 56, 6, 32, 1, 13, 4, 24, 32, 32, 6, 8, 24, 13, 1, 104, 4, 40, 4, 112, 20, 24, 8, 78, 32, 4, 12, 32, 56, 13, 4, 32, 80, 128, 13, 57, 40, 24, 13, 24, 6, 78, 24, 32, 32, 4, 14, 128, 32, 13, 18, 104, 4, 13, 13, 336, 38, 80, 32, 48, 4, 32, 6, 128, 133

Offset: 1

Author

Michel Lagneau, Jul 23 2011

Keywords

• nonn

Comments

sigma(n) = sum of divisors of n: A000203 (also called sigma_1(n)).

Examples

			a(8) = 24 because sigma(8) = 15 and the sum of the 4 odd divisors  { 1, 3, 5, 15} is 24.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Index entries for sequences related to sigma(n).
• Index entries for sequences related to sums of divisors.

Crossrefs

Cf. A000203, A028982, A051027, A193335, A193336.

Programs

Mathematica

Table[Total[Select[Divisors[DivisorSigma[1,n]], OddQ[ # ]&]], {n, 60}]

PARI

a(n) = sumdiv(sigma(n), d, (d%2)*d); \\ Michel Marcus, Jan 14 2014

Formula

a(n) = A000593(A000203(n)). - Michel Marcus, Jan 14 2014

a(n) + A193336(n) = A051027(n). - Antti Karttunen, Nov 18 2017

a(n) = A051027(n) if and only if n is in A028982. - Amiram Eldar, Mar 30 2024

Extensions

More terms from Antti Karttunen, Nov 18 2017