A289624 a(n) = A002322(n)/A007947(A034380(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Jul 17 2017

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65536

Crossrefs

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

Programs

Maple

with(numtheory):
rad := n -> ilcm(op(factorset(n))):
a := n -> lambda(n)/rad(phi(n)/lambda(n)):
seq(a(n), n=1..94); # Peter Luschny, Jul 17 2017

Mathematica

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

PARI

A002322(n) = lcm(znstar(n)[2]); \\ This function from Charles R Greathouse IV, Aug 04 2012
A007947(n) = factorback(factorint(n)[, 1]); \\ This function from Andrew Lelechenko, May 09 2014
A289624(n) = A002322(n)/A007947(eulerphi(n)/A002322(n));

Sage

from sage.crypto.util import carmichael_lambda
def A007947(n): return mul(p for p in prime_divisors(n))
def A000010(n): return euler_phi(n)
def A002322(n): return carmichael_lambda(n)
def A289624(n): return A002322(n)/A007947(A000010(n)/A002322(n))
print([A289624(n) for n in (1..94)]) # Peter Luschny, Jul 17 2017

Formula

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