A193349 Sum of odd divisors of tau(n).

1, 1, 1, 4, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 1, 6, 1, 4, 1, 4, 1, 1, 1, 1, 4, 1, 1, 4, 1, 1, 1, 4, 1, 1, 1, 13, 1, 1, 1, 1, 1, 1, 1, 4, 4, 1, 1, 6, 4, 4, 1, 4, 1, 1, 1, 1, 1, 1, 1, 4, 1, 1, 4, 8, 1, 1, 1, 4, 1, 1, 1, 4, 1, 1, 4, 4, 1, 1, 1, 6, 6, 1, 1, 4, 1, 1

Offset: 1

Author

Michel Lagneau, Jul 23 2011

Keywords

• nonn

Examples

			a(36) = 13 because tau(36) = 9 and the sum of the 3 odd divisors  {1, 3, 9} is 13.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A000593, A036537, A062069, A193348.

Programs

Mathematica

Table[Total[Select[Divisors[DivisorSigma[0,n]], OddQ[ # ]&]], {n, 80}]

PARI

a(n)=sumdiv(sigma(n,0),d,(d%2)*d);

Formula

a(n) = A000593(A000005(n)). - Reinhard Zumkeller, Jul 25 2011

From Amiram Eldar, Aug 12 2024: (Start)

a(n) = 1 if and only if n is in A036537.

a(n) = A062069(n) if and only if n is a square. (End)