A167345 Totally multiplicative sequence with a(p) = (p-1)*(p-2) = p^2-3p+2 for prime p.

1, 0, 2, 0, 12, 0, 30, 0, 4, 0, 90, 0, 132, 0, 24, 0, 240, 0, 306, 0, 60, 0, 462, 0, 144, 0, 8, 0, 756, 0, 870, 0, 180, 0, 360, 0, 1260, 0, 264, 0, 1560, 0, 1722, 0, 48, 0, 2070, 0, 900, 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) = A003958(n) * A166586(n).

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 2/p^2 + 1/p^3 - 2/p^4) = 0.090842681006... . - 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. A003958, A166586.

Sequence in context: A053814 A293260 A095238 * A292496 A285480 A156431

Adjacent sequences: A167342 A167343 A167344 * A167346 A167347 A167348

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved