A193334 Number of even divisors of sigma(n).

0, 0, 2, 0, 2, 4, 3, 0, 0, 3, 4, 4, 2, 6, 6, 0, 3, 0, 4, 4, 5, 6, 6, 8, 0, 4, 6, 6, 4, 9, 5, 0, 8, 4, 8, 0, 2, 8, 6, 6, 4, 10, 4, 8, 4, 9, 8, 4, 0, 0, 9, 3, 4, 12, 9, 12, 8, 6, 8, 12, 2, 10, 6, 0, 8, 12, 4, 6, 10, 12, 9, 0, 2, 4, 4, 8

Offset

1,3

Comments

sigma(n) = sum of divisors of n, A000203.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

a(n) = A183063(A000203(n)). - Amiram Eldar, Mar 22 2024

Example

a(14) = 6 because sigma(14) = 24 and the 6 even divisors are {2, 4, 6, 8, 12, 24}.

Mathematica

a[n_] := Block[{d = Divisors[DivisorSigma[1, n]]}, Count[EvenQ[d], True]]; Table[a[n], {n, 80}]

Prog

(PARI) a(n)=n=sigma(n); if(n%2, 0, numdiv(n/2)) \\ Charles R Greathouse IV, Jul 30 2011

Crossrefs

Cf. A000203, A183063.

Sequence in context: A023987 A021498 A025251 * A185081 A011119 A240747

Adjacent sequences: A193331 A193332 A193333 * A193335 A193336 A193337

Keyword

nonn,easy

Author

Michel Lagneau, Jul 23 2011

Status

approved