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

1,2

Comments

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

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.

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

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A060440 A340527 A021709 * A141567 A254707 A134417

Adjacent sequences: A193334 A193335 A193336 * A193338 A193339 A193340

Keyword

nonn

Author

Michel Lagneau, Jul 23 2011

Extensions

More terms from Antti Karttunen, Nov 18 2017

Status

approved