A193386 Number of even divisors of phi(n).

0, 0, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 4, 2, 3, 3, 4, 2, 3, 3, 4, 2, 2, 3, 4, 4, 3, 4, 4, 3, 4, 4, 4, 4, 6, 4, 6, 3, 6, 4, 6, 4, 4, 4, 6, 2, 2, 4, 4, 4, 5, 6, 4, 3, 6, 6, 6, 4, 2, 4, 8, 4, 6, 5, 8, 4, 4, 5, 4, 6, 4, 6, 9, 6, 6, 6, 8, 6, 4, 5, 4, 6, 2, 6, 6, 4, 6, 6, 6, 6, 9, 4, 8, 2, 9, 5, 10, 4, 8, 6, 6, 5, 4, 8, 8

Offset: 1

Author

Michel Lagneau, Jul 25 2011

Keywords

• nonn

Examples

			a(13) = 4 because phi(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. A000010, A062821, A183063, A191613, A193453.

Programs

Mathematica

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

PARI

A193386(n) = sumdiv(eulerphi(n), d, 1-(d%2)); \\ Antti Karttunen, Dec 04 2017

Formula

a(n) = A183063(A000010(n)) = A062821(n) - A193453(n). - Antti Karttunen, Dec 04 2017

Extensions

More terms from Antti Karttunen, Dec 04 2017