A326069 a(n) = gcd((sigma(n) - sigma(A032742(n))) - n, n - sigma(A032742(n))), where A032742 gives the largest proper divisor of n.

1, 1, 2, 1, 4, 2, 6, 1, 5, 2, 10, 4, 12, 2, 3, 1, 16, 1, 18, 2, 1, 2, 22, 4, 19, 2, 14, 4, 28, 6, 30, 1, 3, 2, 1, 1, 36, 2, 1, 2, 40, 2, 42, 4, 3, 2, 46, 4, 41, 1, 3, 2, 52, 2, 1, 8, 1, 2, 58, 12, 60, 2, 1, 1, 1, 6, 66, 2, 3, 2, 70, 1, 72, 2, 2, 4, 1, 2, 78, 2, 41, 2, 82, 4, 1, 2, 3, 4, 88, 6, 7, 4, 1, 2, 5, 4, 96, 1, 3, 1, 100, 6, 102, 2, 3

Offset: 1

Author

Antti Karttunen, Jun 06 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A032742, A326065, A326066, A326067, A326068.

Cf. also A009194, A325385, A325813, A325975, A326046, A326047, A326048, A326056, A326057, A326060, A326062.

Programs

PARI

A032742(n) = if(1==n,n,n/vecmin(factor(n)[,1]));
A326066(n) = (sigma(n) - sigma(A032742(n)));
A326067(n) = (A326066(n) - n);
A326065(n) = sigma(A032742(n));
A326068(n) = (n - A326065(n));
A326069(n) = gcd(A326067(n), A326068(n));

Formula

a(n) = gcd(A326067(n), A326068(n)) = gcd(A326066(n) - n, n - A326065(n)).