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

1,6

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.

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

Mathematica

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

Prog

(Haskell)
a009194 n = gcd (a000203 n) n  -- Reinhard Zumkeller, Mar 23 2013
(PARI) a(n) = gcd(n, sigma(n)); \\ Michel Marcus, Oct 23 2013

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.

Sequence in context: A325633 A325640 A325632 * A324544 A323160 A323166

Adjacent sequences: A009191 A009192 A009193 * A009195 A009196 A009197

Keyword

nonn

Author

David W. Wilson

Status

approved