A325970 a(n) is the largest k <= A066503(n) such that k and (2n-sigma(n)) [= A033879(n)] are relatively prime.

0, 0, -1, 2, -1, -1, -1, 6, 6, -1, -1, 5, -1, -1, -1, 14, -1, 11, -1, 9, -1, -1, -1, 17, 20, -1, 23, 1, -1, -1, -1, 30, -1, -1, -1, 30, -1, -1, -1, 29, -1, -1, -1, 21, 29, -1, -1, 41, 42, 40, -1, 25, -1, 47, -1, 41, -1, -1, -1, 29, -1, -1, 41, 62, -1, -1, -1, 33, -1, -1, -1, 65, -1, -1, 59, 37, -1, -1, -1, 69, 78

Offset: 1

Author

Antti Karttunen, May 31 2019

Keywords

• sign

Comments

a(n) = n-k for the least k >= A007947(n) such that n-k and n-(sigma(n)-k) are relatively prime.

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, A005117, A007947, A033879, A066503, A324213, A325826, A325960, A325967, A325971, A325972.

Programs

PARI

A007947(n) = factorback(factorint(n)[, 1]); \\ From A007947
A325970(n) = { my(s=sigma(n)); forstep(k=n-A007947(n), -oo, -1, if(1==gcd(k, n+n-sigma(n)), return(k))); };
\\ Or alternatively:
A325970(n) = { my(s=sigma(n)); for(i=A007947(n), s, if(1==gcd(n-i, n-(s-i)), return(n-i))); };

Formula

a(n) = n - A325971(n).

For n >= 3, a(A005117(n)) = -1.