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
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
- N. J. A. Sloane, Transforms.
Programs
-
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 *)
-
PARI
a(n) = sumdiv(n, d, moebius(n/d)*d/core(d, 1)[2]); \\ Michel Marcus, Aug 18 2021
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