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Number of even divisors of phi(n).
3

%I #16 Dec 05 2017 04:08:41

%S 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,

%T 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,

%U 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

%N Number of even divisors of phi(n).

%H Antti Karttunen, <a href="/A193386/b193386.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A183063(A000010(n)) = A062821(n) - A193453(n). - _Antti Karttunen_, Dec 04 2017

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

%t f[n_] := Block[{d = Divisors[EulerPhi[n]]}, Count[EvenQ[d], True]]; Table[f[n], {n, 80}]

%t (* Second program: *)

%t Array[DivisorSum[EulerPhi@ #, 1 &, EvenQ] &, 105] (* _Michael De Vlieger_, Dec 04 2017 *)

%o (PARI) A193386(n) = sumdiv(eulerphi(n), d, 1-(d%2)); \\ _Antti Karttunen_, Dec 04 2017

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

%K nonn

%O 1,5

%A _Michel Lagneau_, Jul 25 2011

%E More terms from _Antti Karttunen_, Dec 04 2017