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A034380 Ratio of totient to Carmichael's lambda function: a(n) = A000010(n) / A002322(n). 26
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,8
COMMENTS
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 if n is a term of A033948, otherwise a(n) > 1 (and n is a term of A033949). - Joerg Arndt, Jul 14 2012
LINKS
W. D. Banks and F. Luca, On integers with a special divisibility property, Archivum Mathematicum (BRNO) 42 (2006) pp 31-42.
FORMULA
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
MAPLE
A034380 := n-> phi(n) / lambda(n);
MATHEMATICA
Table[EulerPhi[n]/CarmichaelLambda[n], {n, 1, 200}] (* Geoffrey Critzer, Dec 23 2014 *)
PROG
(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
CROSSREFS
Sequence in context: A046072 A072273 A157230 * A328966 A077479 A335225
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified February 21 06:16 EST 2024. Contains 370219 sequences. (Running on oeis4.)