A193529 Sum of odd divisors of sopf(n).

0, 1, 4, 1, 6, 6, 8, 1, 4, 8, 12, 6, 14, 13, 1, 1, 18, 6, 20, 8, 6, 14, 24, 6, 6, 24, 4, 13, 30, 6, 32, 1, 8, 20, 4, 6, 38, 32, 1, 8, 42, 4, 44, 14, 1, 31, 48, 6, 8, 8, 6, 24, 54, 6, 1, 13, 12, 32, 60, 6, 62, 48, 6, 1, 13, 1, 68, 20, 14, 8, 72, 6, 74, 56, 1

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A000593(A008472(n)). - Amiram Eldar, May 18 2023

Example

a(5) = 6 because sopf(5) = 5, and the sum of the 2 odd divisors of 5, {1, 5}, is 6.

Mathematica

Table[Total[Select[Divisors[Plus@@First[Transpose[FactorInteger[n]]]], OddQ[#]&]], {n, 100}]
sopf[n_] := Total[FactorInteger[n][[;; , 1]]]; oddsigma[n_] := DivisorSigma[1, n/2^IntegerExponent[n, 2]]; a[1] = 0; a[n_] := oddsigma[sopf[n]]; Array[a, 100] (* Amiram Eldar, May 18 2023 *)

Crossrefs

Cf. A000593, A008472 (sopf), A193523.

Sequence in context: A205325 A021100 A021028 * A214561 A066575 A070251

Adjacent sequences: A193526 A193527 A193528 * A193530 A193531 A193532

Keyword

nonn

Author

Michel Lagneau, Jul 29 2011

Status

approved