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A066715 a(n) = gcd(2n+1, sigma(2n+1)). 5

%I

%S 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,

%T 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,

%U 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

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

%C 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.

%H Harry J. Smith, <a href="/A066715/b066715.txt">Table of n, a(n) for n = 0..1000</a>

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

%o (PARI) forstep (x=3,2000,2,write1("oddperfectgcd.txt",gcd(sigma(x),x),","))

%o (PARI) { for (n=0, 1000, write("b066715.txt", n, " ", gcd(2*n+1, sigma(2*n+1))) ) } \\ _Harry J. Smith_, Mar 19 2010

%K nonn

%O 0,8

%A _Jon Perry_, Jan 14 2002

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Last modified July 20 15:59 EDT 2019. Contains 325185 sequences. (Running on oeis4.)