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A034380
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Ratio of totient to Carmichael's lambda function: a(n) = A000010(n) / A002322(n).
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21
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1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 1, 1, 2, 2, 1, 1, 4, 1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 2, 1, 1, 2, 4, 1, 2, 1, 2, 2, 1, 1, 4, 1, 1, 2, 2, 1, 1, 2, 4, 2, 1, 1, 4, 1, 1, 6, 2, 4, 2, 1, 2, 2, 2, 1, 4, 1, 1, 2, 2, 2, 2, 1, 8, 1, 1, 1, 4, 4, 1, 2, 4, 1, 2, 6, 2, 2, 1, 2, 4, 1, 1, 2, 2, 1, 2, 1, 4, 4
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OFFSET
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1,8
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COMMENTS
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a(n)=1 if and only if the multiplicative group modulo n is cyclic (that is, if n is either 1, 2, 4, or of the form p^k or 2*p^k where p is an odd prime). In other words: a(n)=1 for n is a term of A033948, otherwise a(n)>1 (and n is a term of A033949). [Joerg Arndt, Jul 14 2012]
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
W. D. Banks and F. Luca, On integers with a special divisibility property, Archivum Mathematicum (BRNO) 42 (2006) pp 31-42.
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FORMULA
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a(n) = A000010(n) / A002322(n).
a(A033948(n)) = 1 [Banks & Luca]. - R. J. Mathar, Jul 29 2007
A002322(n)/A007947(a(n)) = A289624(n). - Antti Karttunen, Jul 17 2017
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MAPLE
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A034380 := n-> phi(n) / lambda(n);
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MATHEMATICA
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Table[EulerPhi[n]/CarmichaelLambda[n], {n, 1, 200}] (* Geoffrey Critzer, Dec 23 2014 *)
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PROG
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(PARI) eulerphi(n)/lcm(znstar(n)[2]) \\ Charles R Greathouse IV, Feb 01 2013
(Haskell)
a034380 n = a000010 n `div` a002322 n
-- Reinhard Zumkeller, Sep 02 2014
(MAGMA) [1] cat [EulerPhi(n) div CarmichaelLambda(n): n in [2..100]]; // Vincenzo Librandi, Jul 18 2017
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CROSSREFS
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Cf. A000010, A002322, A033948, A033949, A062373-A062377, A080400, A289624.
Sequence in context: A046072 A072273 A157230 * A328966 A077479 A335225
Adjacent sequences: A034377 A034378 A034379 * A034381 A034382 A034383
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KEYWORD
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nonn
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AUTHOR
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Alex Fink
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STATUS
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approved
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