A289624 - OEIS

%I #21 Mar 07 2020 14:57:16

%S 1,1,2,2,4,2,6,1,6,4,10,1,12,6,2,2,16,6,18,2,3,10,22,1,20,12,18,3,28,

%T 2,30,4,5,16,6,3,36,18,6,2,40,3,42,5,6,22,46,2,42,20,8,6,52,18,10,3,9,

%U 28,58,2,60,30,1,8,6,5,66,8,11,6,70,3,72,36,10,9,15,6,78,2,54,40,82,3,8,42,14,5,88,6,2,11,15,46

%N a(n) = A002322(n)/A007947(A034380(n)).

%H Antti Karttunen, <a href="/A289624/b289624.txt">Table of n, a(n) for n = 1..65536</a>

%F a(n) = A002322(n) / A007947(A034380(n)) = A002322(n) / A007947(A000010(n) / A002322(n)).

%p with(numtheory):

%p rad := n -> ilcm(op(factorset(n))):

%p a := n -> lambda(n)/rad(phi(n)/lambda(n)):

%p seq(a(n), n=1..94); # _Peter Luschny_, Jul 17 2017

%t a007947[n_]:=Last@ Select[Divisors[n], SquareFreeQ[#] &]; Table[Numerator[CarmichaelLambda[n]/a007947[EulerPhi[n]/CarmichaelLambda[n]]], {n, 100}] (* _Indranil Ghosh_, Jul 17 2017 *)

%o (PARI)

%o A002322(n) = lcm(znstar(n)[2]); \\ This function from _Charles R Greathouse IV_, Aug 04 2012

%o A007947(n) = factorback(factorint(n)[, 1]); \\ This function from _Andrew Lelechenko_, May 09 2014

%o A289624(n) = A002322(n)/A007947(eulerphi(n)/A002322(n));

%o (Sage)

%o from sage.crypto.util import carmichael_lambda

%o def A007947(n): return mul(p for p in prime_divisors(n))

%o def A000010(n): return euler_phi(n)

%o def A002322(n): return carmichael_lambda(n)

%o def A289624(n): return A002322(n)/A007947(A000010(n)/A002322(n))

%o print([A289624(n) for n in (1..94)]) # _Peter Luschny_, Jul 17 2017

%Y Cf. A000010, A002322, A007947, A034380, A080400.

%K nonn

%O 1,3

%A _Antti Karttunen_, Jul 17 2017