A167350 Totally multiplicative sequence with a(p) = (p+1)*(p-2) = p^2-p-2 for prime p.

1, 0, 4, 0, 18, 0, 40, 0, 16, 0, 108, 0, 154, 0, 72, 0, 270, 0, 340, 0, 160, 0, 504, 0, 324, 0, 64, 0, 810, 0, 928, 0, 432, 0, 720, 0, 1330, 0, 616, 0, 1638, 0, 1804, 0, 288, 0, 2160, 0, 1600, 0

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = ((p+1)*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+1)*(p(k)-2))^e(k).

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

a(n) = A003959(n) * A166586(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 3/p^3 + 2/p^4) = 0.1140434597... . - Amiram Eldar, Dec 15 2022

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 1)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 10 2016 *)

Crossrefs

Cf. A003959, A166586.

Sequence in context: A233807 A302771 A378618 * A215669 A244310 A334705

Adjacent sequences: A167347 A167348 A167349 * A167351 A167352 A167353

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved