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

1,5

Links

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

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A000010, A062821, A183063, A191613, A193453.

Sequence in context: A078641 A072628 A343901 * A068212 A323015 A105194

Adjacent sequences: A193383 A193384 A193385 * A193387 A193388 A193389

Keyword

nonn

Author

Michel Lagneau, Jul 25 2011

Extensions

More terms from Antti Karttunen, Dec 04 2017

Status

approved