A167315 Totally multiplicative sequence with a(p) = 5*(p-3) for prime p.

1, -5, 0, 25, 10, 0, 20, -125, 0, -50, 40, 0, 50, -100, 0, 625, 70, 0, 80, 250, 0, -200, 100, 0, 100, -250, 0, 500, 130, 0, 140, -3125, 0, -350, 200, 0, 170, -400, 0, -1250, 190, 0, 200, 1000, 0, -500, 220, 0, 400, -500, 0, 1250, 250, 0, 400, -2500, 0, -650, 280

Offset: 1

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• sign
• easy
• mult

Links

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

Crossrefs

Cf. A001222, A165826, A166589.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (5*(p-3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)

Formula

Multiplicative with a(p^e) = (5*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-3))^e(k).

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

a(n) = A165826(n) * A166589(n) = 5^bigomega(n) * A166589(n) = 5^A001222(n) * A166589(n).