A167354 Totally multiplicative sequence with a(p) = (p-2)^2 = p^2-4p+4 for prime p.

1, 0, 1, 0, 9, 0, 25, 0, 1, 0, 81, 0, 121, 0, 9, 0, 225, 0, 289, 0, 25, 0, 441, 0, 81, 0, 1, 0, 729, 0, 841, 0, 81, 0, 225, 0, 1225, 0, 121, 0, 1521, 0, 1681, 0, 9, 0, 2025, 0, 625, 0

Offset

1,5

Links

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

Formula

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

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

a(n) = A166586(n)^2.

Sum_{k=1..n} a(k) ~ c * n^3, where c = 1 / (3 * Product_{p prime} (1 + 4/p^2)) = 0.08140990308... . - 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]^2, {n, 1, 100}] (* G. C. Greubel, Jun 11 2016 *)

Crossrefs

Cf. A166586.

Sequence in context: A007394 A067153 A057405 * A005066 A076262 A167301

Adjacent sequences: A167351 A167352 A167353 * A167355 A167356 A167357

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved