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.

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, 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, 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

Offset

1,3

Comments

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

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, ...

Links

Antti Karttunen, Table of n, a(n) for n = 1..20000

Index entries for sequences related to sigma(n)

Formula

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

Prog

(PARI)
A008833(n) = (n/core(n));
A326053(n) = (sigma(n)-A008833(n));
A326054(n) = (A326053(n)-n);
A326055(n) = (n-A008833(n));
A326056(n) = gcd(A326054(n), A326055(n));

Crossrefs

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

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

Sequence in context: A321794 A075423 A144774 * A365689 A373948 A074720

Adjacent sequences: A326053 A326054 A326055 * A326057 A326058 A326059

Keyword

nonn

Author

Antti Karttunen, Jun 05 2019

Status

approved