A322869 a(n) = A000120(A048675(n)).

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, 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, 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

Offset: 1

Author

Antti Karttunen, Dec 31 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16384
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..65537
• Index entries for sequences related to binary expansion of n
• Index entries for sequences computed from indices in prime factorization

Crossrefs

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

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

Programs

Mathematica

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

PARI

A048675(n) = { my(f = factor(n)); sum(k=1, #f~, f[k, 2]*2^primepi(f[k, 1]))/2; }; \\ From A048675
A322869(n) = hammingweight(A048675(n));

Formula

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

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

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

a(A002110(n)) = n.