A325965 a(n) is the least k >= A020639(n) such that n-k and n-(sigma(n)-k) are relatively prime.

1, 2, 4, 2, 6, 5, 8, 2, 3, 3, 12, 3, 14, 3, 4, 2, 18, 2, 20, 3, 4, 3, 24, 5, 5, 3, 4, 27, 30, 5, 32, 2, 4, 3, 6, 2, 38, 3, 4, 3, 42, 5, 44, 3, 4, 3, 48, 3, 7, 2, 4, 3, 54, 5, 6, 3, 4, 3, 60, 5, 62, 3, 4, 2, 6, 5, 68, 5, 4, 3, 72, 2, 74, 3, 4, 3, 8, 5, 80, 3, 3, 3, 84, 3, 6, 3, 4, 3, 90, 5, 8, 3, 4, 3, 6, 5, 98, 2, 4, 2

Offset: 1

Author

Antti Karttunen, May 29 2019

Keywords

• nonn

Links

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

Crossrefs

Cf. A000203, A000396, A020639, A325817, A325966.

Programs

PARI

A020639(n) = if(1==n, n, factor(n)[1, 1]);
A325965(n) = { my(s=sigma(n)); for(i=A020639(n), s, if(1==gcd(n-i, n-(s-i)), return(i))); };

Formula

a(n) = A000203(n) - A325966(n).

For all n:

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

a(n) >= A325817(n).