A009194 a(n) = gcd(n, sigma(n)).

1, 1, 1, 1, 1, 6, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 3, 1, 2, 1, 2, 1, 12, 1, 2, 1, 28, 1, 6, 1, 1, 3, 2, 1, 1, 1, 2, 1, 10, 1, 6, 1, 4, 3, 2, 1, 4, 1, 1, 3, 2, 1, 6, 1, 8, 1, 2, 1, 12, 1, 2, 1, 1, 1, 6, 1, 2, 3, 2, 1, 3, 1, 2, 1, 4, 1, 6, 1, 2, 1, 2, 1, 28, 1, 2, 3, 4, 1, 18, 7, 4, 1, 2, 5, 12, 1, 1, 3, 1, 1, 6, 1, 2

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Comments

LCM of common divisors of n and sigma(n). It equals n if n is multiply perfect (A007691). - Labos Elemer, Aug 14 2002

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• P. Pollack, On the greatest common divisor of a number and its sum of divisors, Michigan Math. J. Volume 60, Issue 1 (2011), 199-214.

Crossrefs

Cf. A000203, A003624, A007691, A014567, A017666, A063906, A069059, A073802, A082062, A179931, A205523, A216793 (positions of records), A234367, A249917.

Cf. also A009191, A009205, A009242, A274382, A286591, A286594.

Programs

Haskell

a009194 n = gcd (a000203 n) n  -- Reinhard Zumkeller, Mar 23 2013

Mathematica

Table[GCD[n,DivisorSigma[1,n]],{n,110}] (* Harvey P. Dale, Aug 23 2015 *)

PARI

a(n) = gcd(n, sigma(n)); \\ Michel Marcus, Oct 23 2013

Formula

A000005(a(n)) = A073802(n). - Reinhard Zumkeller, Mar 12 2010

A006530(a(n)) = A082062(n). - Reinhard Zumkeller, Jul 10 2011

a(A014567(n)) = 1; A069059(a(n)) > 1. - Reinhard Zumkeller, Mar 23 2013

a(n) = n/A017666(n). - Antti Karttunen, May 22 2017