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

1,6

Links

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

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)

Example

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

Mathematica

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

Prog

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

Crossrefs

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

Sequence in context: A101665 A229951 A165034 * A115862 A296030 A270144

Adjacent sequences: A193344 A193345 A193346 * A193348 A193349 A193350

Keyword

nonn,changed

Author

Michel Lagneau, Jul 23 2011

Status

approved