A191613 - OEIS

%I #31 Dec 17 2017 03:07:54

%S 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,

%T 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,

%U 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

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

%C Lambda is the function in A002322.

%H Antti Karttunen, <a href="/A191613/b191613.txt">Table of n, a(n) for n = 1..16384</a>

%F a(n) = A183063(A002322(n)). - _Michel Marcus_, Mar 18 2016

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

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

%t (* Second program: *)

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

%o (PARI) a(n) = sumdiv(lcm(znstar(n)[2]), d, 1-(d%2)); \\ _Michel Marcus_, Mar 18 2016

%Y Cf. A002322, A183063, A193322, A193386.

%K nonn

%O 1,5

%A _Michel Lagneau_, Jul 22 2011

%E More terms from _Antti Karttunen_, Dec 04 2017