A167359 Totally multiplicative sequence with a(p) = (p+2)*(p-3) = p^2-p-6 for prime p.

1, -4, 0, 16, 14, 0, 36, -64, 0, -56, 104, 0, 150, -144, 0, 256, 266, 0, 336, 224, 0, -416, 500, 0, 196, -600, 0, 576, 806, 0, 924, -1024, 0, -1064, 504, 0, 1326, -1344, 0, -896, 1634, 0, 1800, 1664, 0, -2000, 2156, 0, 1296, -784, 0, 2400, 2750, 0, 1456

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = ((p+2)*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product ((p(k)+2)*(p(k)-3))^e(k).

a(3k) = 0 for k >= 1.

a(n) = A166590(n) * A166589(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 7/p^3 + 6/p^4) = 0.06114270465... . - Amiram Eldar, Dec 15 2022

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); b[1] = 1; b[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*b[n], {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)

Crossrefs

Cf. A166589, A166590.

Sequence in context: A158802 A230280 A030212 * A259491 A292180 A261979

Adjacent sequences: A167356 A167357 A167358 * A167360 A167361 A167362

Keyword

sign,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved