login
a(n) = A000120(A048675(n)).
6

%I #14 Dec 31 2018 13:23:27

%S 0,1,1,1,1,2,1,2,1,2,1,1,1,2,2,1,1,2,1,2,2,2,1,2,1,2,2,2,1,3,1,2,2,2,

%T 2,2,1,2,2,3,1,3,1,2,1,2,1,2,1,2,2,2,1,3,2,3,2,2,1,1,1,2,2,2,2,3,1,2,

%U 2,3,1,3,1,2,2,2,2,3,1,1,1,2,1,2,2,2,2,3,1,2,2,2,2,2,2,3,1,2,2,2,1,3,1,3,3

%N a(n) = A000120(A048675(n)).

%H Antti Karttunen, <a href="/A322869/b322869.txt">Table of n, a(n) for n = 1..16384</a>

%H Antti Karttunen, <a href="/A322869/a322869.txt">Data supplement: n, a(n) computed for n = 1..65537</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

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

%F a(n) = A000120(A048675(n)) = A000120(A322821(n)).

%F a(n) = A001221(A097248(n)) = A001222(A097248(n)).

%F If n is squarefree, then a(n) = A001221(n) = A322862(n).

%F a(A002110(n)) = n.

%t Array[If[# == 1, 0, DigitCount[Total@ Map[#2*2^(PrimePi@ #1 - 1) & @@ # &, FactorInteger[#]], 2, 1]] &, 105] (* _Michael De Vlieger_, Dec 31 2018 *)

%o (PARI)

%o A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; }; \\ From A048675

%o A322869(n) = hammingweight(A048675(n));

%Y Cf. A000120, A001221, A001222, A048675, A097248, A322821, A322862, A322868.

%Y Cf. A002110 (position of the first occurrence of n).

%K nonn

%O 1,6

%A _Antti Karttunen_, Dec 31 2018