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

Author

Jon Perry, Jan 14 2002

Keywords

• nonn

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.

Examples

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

Links

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

Programs

Mathematica

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

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