A193334 - OEIS

%I #13 Mar 22 2024 04:22:59

%S 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,

%T 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,

%U 12,4,6,10,12,9,0,2,4,4,8

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

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

%H Charles R Greathouse IV, <a href="/A193334/b193334.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A183063(A000203(n)). - _Amiram Eldar_, Mar 22 2024

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

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

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

%Y Cf. A000203, A183063.

%K nonn,easy

%O 1,3

%A _Michel Lagneau_, Jul 23 2011