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

1,4

Links

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

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)

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A370130 A010326 A196879 * A380587 A053231 A066701

Adjacent sequences: A193346 A193347 A193348 * A193350 A193351 A193352

Keyword

nonn

Author

Michel Lagneau, Jul 23 2011

Status

approved