A167339 Totally multiplicative sequence with a(p) = p*(p-2) = p^2-2p for prime p.

1, 0, 3, 0, 15, 0, 35, 0, 9, 0, 99, 0, 143, 0, 45, 0, 255, 0, 323, 0, 105, 0, 483, 0, 225, 0, 27, 0, 783, 0, 899, 0, 297, 0, 525, 0, 1295, 0, 429, 0, 1599, 0, 1763, 0, 135, 0, 2115, 0, 1225, 0

Offset

1,3

Links

G. C. Greubel, Table of n, a(n) for n = 1..1000

Formula

Multiplicative with a(p^e) = (p*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (p(k)*(p(k)-2))^e(k).

a(2k) = 0 for k >= 1.

a(n) = n * A166586(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 1/p^2 + 2/p^3) = 0.1016391193... . - Amiram Eldar, Dec 15 2022

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*n, {n, 1, 100}] (* G. C. Greubel, Jun 08 2016 *)

Crossrefs

Cf. A166586.

Sequence in context: A275831 A065121 A334824 * A277936 A138540 A123023

Adjacent sequences: A167336 A167337 A167338 * A167340 A167341 A167342

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved