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A326056 a(n) = gcd(sigma(n)-A008833(n)-n, n-A008833(n)), where sigma is the sum of divisors of n, and A008833 is the largest square dividing n.

%I A326056 #13 Jun 10 2019 17:55:47
%S A326056 1,1,2,1,4,5,6,1,5,1,10,4,12,1,2,1,16,3,18,2,10,1,22,4,19,5,2,24,28,1,
%T A326056 30,1,2,1,2,19,36,1,2,2,40,1,42,4,12,5,46,4,41,1,10,6,52,3,2,4,2,1,58,
%U A326056 8,60,1,2,1,2,1,66,2,2,1,70,3,72,1,2,12,2,1,78,2,41,1,82,8,2,5,2,4,88,27,10,8,2,1,2,20,96,1,6
%N A326056 a(n) = gcd(sigma(n)-A008833(n)-n, n-A008833(n)), where sigma is the sum of divisors of n, and A008833 is the largest square dividing n.
%C A326056 Composite numbers n such that a(n) = A326055(n) start as: 6, 28, 336, 496, 792, 8128, 31968, 3606912, ...
%C A326056 Nonsquare odd numbers n such that a(n) = abs(A326054(n)) start as: 21, 153, 301, 697, 1333, 1909, 1917, 2041, 3901, 4753, 24601, 24957, 26977, 29161, 29637, 56953, 67077, 96361, ...
%H A326056 Antti Karttunen, <a href="/A326056/b326056.txt">Table of n, a(n) for n = 1..20000</a>
%H A326056 <a href="/index/Si#SIGMAN">Index entries for sequences related to sigma(n)</a>
%F A326056 a(n) = gcd(A326054(n), A326055(n)) = gcd((A000203(n)-A008833(n))-n, n-A008833(n)).
%o A326056 (PARI)
%o A326056 A008833(n) = (n/core(n));
%o A326056 A326053(n) = (sigma(n)-A008833(n));
%o A326056 A326054(n) = (A326053(n)-n);
%o A326056 A326055(n) = (n-A008833(n));
%o A326056 A326056(n) = gcd(A326054(n), A326055(n));
%Y A326056 Cf. A000203, A008833, A326053, A326054, A326055.
%Y A326056 Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326057, A326060, A326062, A326129, A326130, A326140, A326144.
%K A326056 nonn
%O A326056 1,3
%A A326056 _Antti Karttunen_, Jun 05 2019