A325818 a(n) is the largest k <= sigma(n) such that n-k and n-(sigma(n)-k) are relatively prime.

1, 3, 4, 7, 6, 7, 8, 15, 13, 17, 12, 27, 14, 23, 22, 31, 18, 38, 20, 41, 32, 35, 24, 59, 31, 39, 40, 29, 30, 71, 32, 63, 46, 53, 48, 91, 38, 59, 56, 89, 42, 95, 44, 83, 76, 69, 48, 123, 57, 93, 70, 95, 54, 119, 72, 119, 80, 89, 60, 167, 62, 95, 104, 127, 84, 143, 68, 125, 94, 143, 72, 194, 74, 113, 124, 137, 96

Offset: 1

Author

Antti Karttunen, May 29 2019

Keywords

• nonn

Comments

a(n) is the largest k <= sigma(n) such that (-n + k) and (n-sigma(n))+k are coprime.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to sigma(n)

Crossrefs

Cf. A000203, A000396, A324213, A325817, A325826, A325961, A325966, A325968.

Programs

PARI

A325818(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(s-i))); };

Formula

a(n) = A000203(n) - A325817(n).

a(n) = n + A325826(n).

For all n:

a(A000396(n)) = A000396(n)+1.

a(n) >= A325961(n).

a(n) >= A325966(n).

a(n) >= A325968(n).