A193347 - OEIS

%I #17 Jan 27 2025 02:22:49

%S 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,

%T 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,

%U 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

%N Number of even divisors of tau(n).

%H Antti Karttunen, <a href="/A193347/b193347.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A183063(A000005(n)). - _Antti Karttunen_, May 28 2017

%F From _Amiram Eldar_, Jan 27 2025: (Start)

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

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

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

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

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

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

%K nonn

%O 1,6

%A _Michel Lagneau_, Jul 23 2011