A326056 - OEIS

%I #13 Jun 10 2019 17:55:47

%S 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 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 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 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 Composite numbers n such that a(n) = A326055(n) start as: 6, 28, 336, 496, 792, 8128, 31968, 3606912, ...

%C 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 Antti Karttunen, <a href="/A326056/b326056.txt">Table of n, a(n) for n = 1..20000</a>

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

%F a(n) = gcd(A326054(n), A326055(n)) = gcd((A000203(n)-A008833(n))-n, n-A008833(n)).

%o (PARI)

%o A008833(n) = (n/core(n));

%o A326053(n) = (sigma(n)-A008833(n));

%o A326054(n) = (A326053(n)-n);

%o A326055(n) = (n-A008833(n));

%o A326056(n) = gcd(A326054(n), A326055(n));

%Y Cf. A000203, A008833, A326053, A326054, A326055.

%Y Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326057, A326060, A326062, A326129, A326130, A326140, A326144.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jun 05 2019