A317946 Additive with a(p^e) = A011371(e); the 2-adic valuation of A317934(n).

0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 1, 0, 0, 0, 1, 1, 0, 1, 1, 0, 0, 0, 3, 0, 0, 0, 2, 0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 3, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, 0, 1, 4, 0, 0, 0, 1, 0, 0, 0, 2, 0, 0, 1, 1, 0, 0, 0, 3, 3, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 3, 0, 1, 1, 2, 0, 0, 0, 1, 0

Offset

1,16

Comments

Records are A005187, occurring at A000302 (powers of 4).

Links

Antti Karttunen, Table of n, a(n) for n = 1..65537

Formula

a(n) = A007814(A317934(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = Sum_{p prime, k>=1} 1/(p^(2^k) - 1) = 0.63710219855356676263... . - Amiram Eldar, Jan 21 2024

Mathematica

f[p_, e_] := e - DigitCount[e, 2, 1]; a[1] = 0; a[n_] := Plus @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Jan 21 2024 *)

Prog

(PARI)
A011371(n) = (n - hammingweight(n));
A317934(n) = vecsum(apply(e -> A011371(e), factor(n)[, 2]));

Crossrefs

Cf. A000302, A005187, A011371, A317934.

Cf. also A046645.

Sequence in context: A372503 A318499 A346012 * A347439 A347048 A374213

Adjacent sequences: A317943 A317944 A317945 * A317947 A317948 A317949

Keyword

nonn

Author

Antti Karttunen, Aug 24 2018

Status

approved