A346612 Moebius transform of A019554.

1, 1, 2, 0, 4, 2, 6, 2, 0, 4, 10, 0, 12, 6, 8, 0, 16, 0, 18, 0, 12, 10, 22, 4, 0, 12, 6, 0, 28, 8, 30, 4, 20, 16, 24, 0, 36, 18, 24, 8, 40, 12, 42, 0, 0, 22, 46, 0, 0, 0, 32, 0, 52, 6, 40, 12, 36, 28, 58, 0, 60, 30, 0, 0, 48, 20, 66, 0, 44, 24, 70, 0, 72, 36, 0, 0, 60, 24, 78, 0, 0

Offset

1,3

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

N. J. A. Sloane, Transforms.

Formula

Multiplicative with a(p^e) = 0 if e is even, and p^((e+1)/2) - p^((e-1)/2) if e is odd. - Amiram Eldar, Aug 19 2021

Sum_{k=1..n} a(k) ~ c * n^2, where c = 18*zeta(3)/Pi^4 = 0.222125... . - Amiram Eldar, Nov 18 2022

Mathematica

f[p_, e_] := If[EvenQ[e], 0, p^((e + 1)/2) - p^((e - 1)/2)]; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Aug 19 2021 *)

Prog

(PARI) a(n) = sumdiv(n, d, moebius(n/d)*d/core(d, 1)[2]); \\ Michel Marcus, Aug 18 2021

Crossrefs

Cf. A002117, A019554, A346613.

Sequence in context: A083218 A203908 A334082 * A352528 A307704 A139716

Adjacent sequences: A346609 A346610 A346611 * A346613 A346614 A346615

Keyword

nonn,mult,easy

Author

N. J. A. Sloane, Aug 18 2021

Status

approved