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A034380 Ratio of totient to Carmichael's lambda function: a(n) = A000010(n) / A002322(n). 21
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 for n is a term of A033948, otherwise a(n)>1 (and n is a term of A033949). [Joerg Arndt, Jul 14 2012]

LINKS

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.

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

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

KEYWORD

nonn

AUTHOR

Alex Fink

STATUS

approved

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Last modified November 27 08:53 EST 2020. Contains 338679 sequences. (Running on oeis4.)