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A009194
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a(n) = gcd(n, sigma(n)).
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38
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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
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OFFSET
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1,6
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COMMENTS
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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
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LINKS
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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.
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FORMULA
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a(n) = n/A017666(n). - Antti Karttunen, May 22 2017
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MAPLE
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seq(gcd(sigma(n), n), n=1..104); # Paolo P. Lava, May 16 2018
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MATHEMATICA
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Table[GCD[n, DivisorSigma[1, n]], {n, 110}] (* Harvey P. Dale, Aug 23 2015 *)
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PROG
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(Haskell)
a009194 n = gcd (a000203 n) n -- Reinhard Zumkeller, Mar 23 2013
(PARI) a(n) = gcd(n, sigma(n)); \\ Michel Marcus, Oct 23 2013
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson
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STATUS
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approved
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