cp's OEIS Frontend

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

%I A034380 #51 Jan 19 2023 02:31:38
%S A034380 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,
%T A034380 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,
%U A034380 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
%N A034380 Ratio of totient to Carmichael's lambda function: a(n) = A000010(n) / A002322(n).
%C A034380 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
%H A034380 T. D. Noe, <a href="/A034380/b034380.txt">Table of n, a(n) for n = 1..10000</a>
%H A034380 W. D. Banks and F. Luca, <a href="https://www.emis.de/journals/AM/06-1/am1278.pdf">On integers with a special divisibility property</a>, Archivum Mathematicum (BRNO) 42 (2006) pp 31-42.
%F A034380 a(n) = A000010(n) / A002322(n).
%F A034380 a(A033948(n)) = 1 [Banks & Luca]. - _R. J. Mathar_, Jul 29 2007
%F A034380 A002322(n)/A007947(a(n)) = A289624(n). - _Antti Karttunen_, Jul 17 2017
%p A034380 A034380 := n-> phi(n) / lambda(n);
%t A034380 Table[EulerPhi[n]/CarmichaelLambda[n], {n, 1, 200}] (* _Geoffrey Critzer_, Dec 23 2014 *)
%o A034380 (PARI) eulerphi(n)/lcm(znstar(n)[2]) \\ _Charles R Greathouse IV_, Feb 01 2013
%o A034380 (Haskell)
%o A034380 a034380 n = a000010 n `div` a002322 n
%o A034380 -- _Reinhard Zumkeller_, Sep 02 2014
%o A034380 (Magma) [1] cat [EulerPhi(n) div CarmichaelLambda(n): n in [2..100]]; // _Vincenzo Librandi_, Jul 18 2017
%Y A034380 Cf. A000010, A002322, A033948, A033949, A062373-A062377, A080400, A289624.
%K A034380 nonn
%O A034380 1,8
%A A034380 _Alex Fink_