A325826 a(n) is the largest k <= sigma(n)-n such that k and (2n-sigma(n)) [= A033879(n)] are relatively prime.

0, 1, 1, 3, 1, 1, 1, 7, 4, 7, 1, 15, 1, 9, 7, 15, 1, 20, 1, 21, 11, 13, 1, 35, 6, 13, 13, 1, 1, 41, 1, 31, 13, 19, 13, 55, 1, 21, 17, 49, 1, 53, 1, 39, 31, 23, 1, 75, 8, 43, 19, 43, 1, 65, 17, 63, 23, 31, 1, 107, 1, 33, 41, 63, 19, 77, 1, 57, 25, 73, 1, 122, 1, 39, 49, 61, 19, 89, 1, 105, 40, 43, 1, 139, 23, 43, 31, 91, 1, 143, 19, 75

Offset

1,4

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)

Formula

a(n) = A325818(n) - n = A001065(n) - A325817(n) = A325976(n) - A033879(n).

a(A000040(n)) = a(A000396(n)) = 1.

a(n) >= A325969(n).

gcd(a(n), A325976(n)) = 1.

Prog

(PARI) A325826(n) = { my(s=sigma(n)); forstep(k=s-n, 0, -1, if(1==gcd((n+n-sigma(n)), k), return(k))); };
(PARI)
A325818(n) = { my(s=sigma(n)); for(i=0, s, if(1==gcd(n-i, n-(s-i)), return(s-i))); };
A325826(n) = (A325818(n) - n);

Crossrefs

Cf. A000040, A000203, A000396, A001065, A033879, A324213, A325817, A325818, A325969, A325970, A325976.

Sequence in context: A335341 A243473 A325969 * A081297 A110180 A328718

Adjacent sequences: A325823 A325824 A325825 * A325827 A325828 A325829

Keyword

nonn

Author

Antti Karttunen, May 29 2019

Status

approved