%I #10 May 09 2018 23:03:04

%S 0,1,2,1,3,3,4,1,4,4,5,3,6,5,5,1,7,5,8,4,6,6,9,3,9,7,8,5,10,6,11,1,7,

%T 8,7,5,12,9,8,4,13,7,14,6,7,10,15,3,16,10,9,7,16,9,8,5,10,11,17,6,18,

%U 12,8,1,9,8,19,8,11,8,20,5,21,13,11,9,9,9,22,4,16,14,23,7,10,15,12,6

%N If n = Product (p_j^k_j) then a(n) = Sum (pi(p_j)^k_j), where pi() = A000720.

%H Ilya Gutkovskiy, <a href="/A304037/a304037.pdf">Extended graphical example</a>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F If gcd(u,v) = 1 then a(u*v) = a(u) + a(v).

%F a(p^k) = A000720(p)^k where p is a prime.

%F a(A002110(m)^k) = 1^k + 2^k + ... + m^k.

%F As an example:

%F a(A000040(k)) = k.

%F a(A006450(k)) = A000040(k).

%F a(A038580(k)) = A006450(k).

%F a(A001248(k)) = a(A011757(k)) = A000290(k).

%F a(A030078(k)) = a(A055875(k)) = A000578(k).

%F a(A002110(k)) = a(A011756(k)) = A000217(k).

%F a(A061742(k)) = A000330(k).

%F a(A115964(k)) = A000537(k).

%F a(A080696(k)) = A007504(k).

%F a(A076954(k)) = A001923(k).

%e a(72) = 5 because 72 = 2^3*3^2 = prime(1)^3*prime(2)^2 and 1^3 + 2^2 = 5.

%t a[n_] := Plus @@ (PrimePi[#[[1]]]^#[[2]]& /@ FactorInteger[n]); a[1] = 0; Table[a[n], {n, 1, 88}]

%Y Cf. A000040, A000720, A002110, A003963, A008475, A056239, A066328, A156061, A222416.

%K nonn

%O 1,3

%A _Ilya Gutkovskiy_, May 05 2018