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A317946
Additive with a(p^e) = A011371(e); the 2-adic valuation of A317934(n).
5
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
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. also A046645.
Sequence in context: A372503 A318499 A346012 * A347439 A347048 A374213
KEYWORD
nonn
AUTHOR
Antti Karttunen, Aug 24 2018
STATUS
approved