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A009194 a(n) = gcd(n, sigma(n)). 36
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,6

COMMENTS

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

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

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

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

MAPLE

seq(gcd(sigma(n), n), n=1..104); # Paolo P. Lava, May 16 2018

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: A080219 A293901 A040037 * A007732 A237835 A126795

Adjacent sequences:  A009191 A009192 A009193 * A009195 A009196 A009197

KEYWORD

nonn

AUTHOR

David W. Wilson

STATUS

approved

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Last modified September 25 22:57 EDT 2018. Contains 315425 sequences. (Running on oeis4.)