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A009195
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GCD(n, phi(n)).
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19
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1, 1, 1, 2, 1, 2, 1, 4, 3, 2, 1, 4, 1, 2, 1, 8, 1, 6, 1, 4, 3, 2, 1, 8, 5, 2, 9, 4, 1, 2, 1, 16, 1, 2, 1, 12, 1, 2, 3, 8, 1, 6, 1, 4, 3, 2, 1, 16, 7, 10, 1, 4, 1, 18, 5, 8, 3, 2, 1, 4, 1, 2, 9, 32, 1, 2, 1, 4, 1, 2, 1, 24, 1, 2, 5, 4, 1, 6, 1, 16, 27, 2, 1, 12, 1, 2, 1, 8, 1, 6, 1, 4, 3, 2, 1, 32, 1, 14, 3, 20
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| The inequality gcd(n, phi(n)) <= 2n exp(-sqrt(log 2 log n)) holds for all squarefree n >= 1 (Erdos, Luca, and Pomerance).
Erdős shows that for almost all n, a(n) ~ log log log log n. [Charles R Greathouse IV, Nov 23 2011]
Also GCD[n, A051593[n]] (Labos E.).
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LINKS
| T. D. Noe, Table of n, a(n) for n = 1..10000
Paul Erdős, Some asymptotic formulas in number theory, J. Indian Math. Soc. (N.S.) 12 (1948), pp. 75-78.
Paul Erdos, Florian Luca, Carl Pomerance, On the proportion of numbers coprime to a given integer, in Anatomy of Integers, pp. 47--64, J.-M. De Koninck, A. Granville, F. Luca (editors), AMS, 2008.
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MAPLE
| a009195 := n -> igcd(i, numtheory[phi](n));
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MATHEMATICA
| Table[GCD[n, EulerPhi[n]], {n, 100}] (* From Harvey P. Dale, Aug 11 2011 *)
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PROG
| (PARI) a(n)=gcd(n, eulerphi(n)) \\ Charles R Greathouse IV, Nov 23 2011
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CROSSREFS
| Cf. A000010, A003277, A050399.
Sequence in context: A171453 A164879 A200219 * A072994 A052126 A094521
Adjacent sequences: A009192 A009193 A009194 * A009196 A009197 A009198
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KEYWORD
| nonn,easy,nice
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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