A325817 a(n) is the least k >= 0 such that n-k and n-(sigma(n)-k) are relatively prime.

0, 0, 0, 0, 0, 5, 0, 0, 0, 1, 0, 1, 0, 1, 2, 0, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 0, 27, 0, 1, 0, 0, 2, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 1, 2, 3, 0, 1, 0, 0, 2, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 2, 1, 0, 1, 0, 1, 0, 3, 0, 1, 0, 1, 0, 1, 0, 1, 0, 3, 2, 1, 0, 1, 2, 1, 0, 1, 2, 5, 0, 0, 2, 0, 0, 1, 0, 1, 2

Offset

1,6

Comments

a(n) is the least k >= 0 such that -n + k and (n-sigma(n))+k are coprime.

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Index entries for sequences related to sigma(n)

Formula

a(n) = A000203(n) - A325818(n) = A001065(n) - A325826(n) = n - A325976(n).

For all n:

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

a(n) <= n-1.

a(n) <= A325965(n).

a(n) <= A325967(n).

Example

For n=15, gcd(15-0, 15-(24-0)) = 3, gcd(15-1, 15-(24-1)) = 2 and gcd(15-2, 15-(24-2)) = 1, thus a(15) = 2.

Prog

(PARI) A325817(n) = { my(s=sigma(n)); for(k=0, s, if(1==gcd(-n + k, (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))); };

Crossrefs

Cf. A000203, A000396, A001065, A009194, A014567 (positions of zeros), A324213, A325818, A325826, A325962, A325965, A325967, A325976.

Sequence in context: A368863 A090750 A324656 * A325967 A229656 A216722

Adjacent sequences: A325814 A325815 A325816 * A325818 A325819 A325820

Keyword

nonn

Author

Antti Karttunen, May 29 2019

Status

approved