A066715 a(n) = gcd(2n+1, sigma(2n+1)).

1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 7, 1, 5, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 13, 1, 1, 3, 1, 1, 1, 1, 1, 15, 1, 1, 3, 1, 5, 3, 1, 1, 9, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3

Offset

0,8

Comments

If gcd(n, sigma(n))=1 then n is an odd perfect number. It seems however that gcd(n, sigma(n)) is always significantly less than n.

Links

Harry J. Smith, Table of n, a(n) for n = 0..1000

Example

a(5) = 1 as gcd(5,6) = 1. a(15) = gcd(15, sigma(15)) = gcd(15,(1+3+5+15)) = gcd(15,24) = 3.

Mathematica

Table[GCD[2n+1, DivisorSigma[1, 2n+1]], {n, 0, 120}] (* Harvey P. Dale, Jul 22 2019 *)

Prog

(PARI) forstep (x=3, 2000, 2, write1("oddperfectgcd.txt", gcd(sigma(x), x), ", "))
(PARI) { for (n=0, 1000, write("b066715.txt", n, " ", gcd(2*n+1, sigma(2*n+1))) ) } \\ Harry J. Smith, Mar 19 2010

Crossrefs

Sequence in context: A101874 A318449 A336651 * A082457 A356307 A356306

Adjacent sequences: A066712 A066713 A066714 * A066716 A066717 A066718

Keyword

nonn

Author

Jon Perry, Jan 14 2002

Status

approved