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

1,6

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

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.

Mathematica

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

Prog

(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));

Crossrefs

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

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

Sequence in context: A103587 A306446 A100387 * A229344 A210501 A307781

Adjacent sequences: A322866 A322867 A322868 * A322870 A322871 A322872

Keyword

nonn

Author

Antti Karttunen, Dec 31 2018

Status

approved