A193347 Number of even divisors of tau(n).

0, 1, 1, 0, 1, 2, 1, 2, 0, 2, 1, 2, 1, 2, 2, 0, 1, 2, 1, 2, 2, 2, 1, 3, 0, 2, 2, 2, 1, 3, 1, 2, 2, 2, 2, 0, 1, 2, 2, 3, 1, 3, 1, 2, 2, 2, 1, 2, 0, 2, 2, 2, 1, 3, 2, 3, 2, 2, 1, 4, 1, 2, 2, 0, 2, 3, 1, 2, 2, 3, 1, 4, 1, 2, 2, 2, 2, 3, 1, 2, 0, 2, 1, 4, 2, 2, 2, 3, 1, 4, 2, 2, 2, 2, 2, 4, 1, 2, 2, 0, 1, 3, 1, 3, 3, 2, 1, 4, 1, 3, 2, 2, 1, 3

Offset: 1

Author

Michel Lagneau, Jul 23 2011

Keywords

• nonn

Examples

			a(24) = 3 because tau(24) = 8 and the 3 even divisors are {2, 4, 8}.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A010553, A183063, A193348, A193350.

Programs

Mathematica

f[n_] := Block[{d = Divisors[DivisorSigma[0,n]]}, Count[EvenQ[d], True]]; Table[f[n], {n, 80}]

PARI

a(n)=sumdiv(sigma(n,0),d,(1-d%2));

Formula

a(n) = A183063(A000005(n)). - Antti Karttunen, May 28 2017

From Amiram Eldar, Jan 27 2025: (Start)

a(n) = 0 if and only if n is a square.

a(n) = A010553(n) - A193348(n). (End)