A167361 Totally multiplicative sequence with a(p) = (p-3)^2 = p^2-6p+9 for prime p.

1, 1, 0, 1, 4, 0, 16, 1, 0, 4, 64, 0, 100, 16, 0, 1, 196, 0, 256, 4, 0, 64, 400, 0, 16, 100, 0, 16, 676, 0, 784, 1, 0, 196, 64, 0, 1156, 256, 0, 4, 1444, 0, 1600, 64, 0, 400, 1936, 0, 256, 16, 0, 100, 2500, 0, 256, 16, 0, 676, 3136, 0, 3364, 784, 0, 1, 400

Offset

1,5

Links

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

Formula

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

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

a(n) = A166589(n)^2.

Sum_{k=1..n} a(k) ~ c * n^3, where c = (2/Pi^2) / Product_{p prime} (1 + 5/p^2 - 3/p^3 - 9/p^4) = 0.07909568395... . - Amiram Eldar, Dec 15 2022

Mathematica

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

Crossrefs

Cf. A166589.

Sequence in context: A003195 A190759 A086262 * A321610 A167314 A208451

Adjacent sequences: A167358 A167359 A167360 * A167362 A167363 A167364

Keyword

nonn,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved