A325976 a(n) is the largest k <= n such that k and (2n-sigma(n)) [= A033879(n)] are relatively prime.

1, 2, 3, 4, 5, 1, 7, 8, 9, 9, 11, 11, 13, 13, 13, 16, 17, 17, 19, 19, 21, 21, 23, 23, 25, 23, 27, 1, 29, 29, 31, 32, 31, 33, 35, 36, 37, 37, 39, 39, 41, 41, 43, 43, 43, 43, 47, 47, 49, 50, 49, 49, 53, 53, 55, 55, 57, 57, 59, 59, 61, 61, 63, 64, 65, 65, 67, 67, 67, 69, 71, 71, 73, 73, 75, 73, 77, 77, 79, 79, 81, 81, 83, 83, 85, 83

Offset: 1

Author

Antti Karttunen, Jun 01 2019

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16385
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A033879, A325817, A325818, A325826, A325959.

Programs

PARI

A325976(n) = { my(s=sigma(n)); forstep(k=n, 0, -1, if(1==gcd((n+n-s), k), return(k))); };

PARI

A325817(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(i))); };
A325976(n) = (n - A325817(n));

Formula

a(n) = n - A325817(n) = A033879(n) + A325826(n).

a(n) >= A325959(n).

gcd(a(n), A325826(n)) = 1.