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Sum of even divisors of sigma(n).
2

%I #15 Mar 30 2024 03:01:49

%S 0,0,6,0,8,24,14,0,0,26,24,48,16,56,56,0,26,0,36,64,62,78,56,144,0,64,

%T 84,112,48,182,62,0,120,80,120,0,40,144,112,156,64,248,72,192,112,182,

%U 120,192,0,0,182,114,80,336,182,336,180,156,144,448,64,248,196,0,192,390,108,208,248,390,182,0,76,160,192,288,248,448,180,256,0

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

%C sigma(n) = sum of divisors of n: A000203 (also called sigma_1(n)).

%H Antti Karttunen, <a href="/A193336/b193336.txt">Table of n, a(n) for n = 1..16384</a>

%H <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>.

%H <a href="/index/Su#sums_of_divisors">Index entries for sequences related to sums of divisors</a>.

%F a(n) + A193337(n) = A051027(n). - _Antti Karttunen_, Nov 18 2017

%F From _Amiram Eldar_, Mar 30 2024: (Start)

%F a(n) = A146076(A000203(n)).

%F a(n) = 0 if and only if n is in A028982. (End)

%e a(14) = 56 because sigma(14) = 24 and the sum of the 6 even divisors {2, 4, 6, 8, 12, 24} is 56.

%t Table[Total[Select[Divisors[DivisorSigma[1,n]], EvenQ[ # ]&]], {n, 53}]

%o (PARI) A193336(n) = { my(s=sigma(n)); sumdiv(s,d,(!(d%2))*d); }; \\ _Antti Karttunen_, Nov 18 2017

%Y Cf. A000203, A028982, A051027, A146076, A193334, A193337.

%K nonn

%O 1,3

%A _Michel Lagneau_, Jul 23 2011

%E More terms from _Antti Karttunen_, Nov 18 2017