A220345 Ratio of Jordan's totient to Carmichael's lambda function: a(n) = A007434(n) / A002322(n).

1, 3, 4, 6, 6, 12, 8, 24, 12, 18, 12, 48, 14, 24, 48, 48, 18, 36, 20, 72, 64, 36, 24, 192, 30, 42, 36, 96, 30, 144, 32, 96, 96, 54, 96, 144, 38, 60, 112, 288, 42, 192, 44, 144, 144, 72, 48, 384, 56, 90, 144, 168, 54, 108, 144, 384, 160, 90, 60, 576, 62, 96

Offset: 1

Author

Enrique Pérez Herrero, Dec 11 2012

Keywords

• nonn

Comments

a(n) is always integer because lambda(n) divides phi(n), and phi(n) divides J_2(n).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001615, A002322, A007434, A034380.

Programs

Mathematica

jordanTotient[n_, k_: 1] := DivisorSum[n, #^k*MoebiusMu[n/#] &] /; (n > 0) && IntegerQ[n]; Table[jordanTotient[n, 2]/CarmichaelLambda[n], {n, 100}] (* T. D. Noe, Dec 11 2012 *)

Formula

a(n) = A007434(n) / A002322(n) = A034380(n) * A001615(n).