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

Author

Michel Lagneau, Jul 23 2011

Keywords

• nonn
• easy

Comments

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

Examples

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

Links

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

Crossrefs

Cf. A000203, A183063.

Programs

Mathematica

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

PARI

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

Formula

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