A034380 Ratio of totient to Carmichael's lambda function: a(n) = A000010(n) / A002322(n).

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

Offset: 1

Author

Alex Fink

Keywords

• nonn

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

• 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.

Crossrefs

Cf. A000010, A002322, A033948, A033949, A062373-A062377, A080400, A289624.

Programs

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

Maple

A034380 := n-> phi(n) / lambda(n);

Mathematica

Table[EulerPhi[n]/CarmichaelLambda[n], {n, 1, 200}] (* Geoffrey Critzer, Dec 23 2014 *)

PARI

eulerphi(n)/lcm(znstar(n)[2]) \\ Charles R Greathouse IV, Feb 01 2013

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