A191613 Number of even divisors of lambda(n).

0, 0, 1, 1, 2, 1, 2, 1, 2, 2, 2, 1, 4, 2, 2, 2, 4, 2, 3, 2, 2, 2, 2, 1, 4, 4, 3, 2, 4, 2, 4, 3, 2, 4, 4, 2, 6, 3, 4, 2, 6, 2, 4, 2, 4, 2, 2, 2, 4, 4, 4, 4, 4, 3, 4, 2, 3, 4, 2, 2, 8, 4, 2, 4, 4, 2, 4, 4, 2, 4, 4, 2, 9, 6, 4, 3, 4, 4, 4, 2, 4, 6, 2, 2, 4, 4, 4, 2, 6, 4, 4, 2, 4, 2, 6, 3, 10, 4, 4, 4, 6, 4, 4, 4, 4

Offset: 1

Author

Michel Lagneau, Jul 22 2011

Keywords

• nonn

Comments

Lambda is the function in A002322.

Examples

			a(13) = 4 because lambda(13) = 12 and the 4 even divisors are { 2, 4, 6, 12}.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384

Crossrefs

Cf. A002322, A183063, A193322, A193386.

Programs

Mathematica

f[n_] := Block[{d = Divisors[CarmichaelLambda[n]]}, Count[EvenQ[d], True]]; Table[f[n], {n, 80}]
(* Second program: *)
Array[DivisorSum[CarmichaelLambda@ #, 1 &, EvenQ] &, 105] (* Michael De Vlieger, Dec 04 2017 *)

PARI

a(n) = sumdiv(lcm(znstar(n)[2]), d, 1-(d%2)); \\ Michel Marcus, Mar 18 2016

Formula

a(n) = A183063(A002322(n)). - Michel Marcus, Mar 18 2016

Extensions

More terms from Antti Karttunen, Dec 04 2017