A167320 Totally multiplicative sequence with a(p) = 10*(p-3) for prime p.

1, -10, 0, 100, 20, 0, 40, -1000, 0, -200, 80, 0, 100, -400, 0, 10000, 140, 0, 160, 2000, 0, -800, 200, 0, 400, -1000, 0, 4000, 260, 0, 280, -100000, 0, -1400, 800, 0, 340, -1600, 0, -20000, 380, 0, 400, 8000, 0, -2000, 440, 0, 1600, -4000, 0, 10000, 500, 0, 1600

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, A165831, A166589.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*10^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (10*(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) = (10*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-3))^e(k).

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

a(n) = A165831(n) * A166589(n) = 10^bigomega(n) * A166589(n) = 10^A001222(n) * A166589(n).