A167317 Totally multiplicative sequence with a(p) = 7*(p-3) for prime p.

1, -7, 0, 49, 14, 0, 28, -343, 0, -98, 56, 0, 70, -196, 0, 2401, 98, 0, 112, 686, 0, -392, 140, 0, 196, -490, 0, 1372, 182, 0, 196, -16807, 0, -686, 392, 0, 238, -784, 0, -4802, 266, 0, 280, 2744, 0, -980, 308, 0, 784, -1372, 0, 3430, 350, 0, 784, -9604, 0, -1274

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, A165828, A166589.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 3)^fi[[All, 2]])); Table[a[n]*7^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (7*(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) = (7*(p-3))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)-3))^e(k).

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

a(n) = A165828(n) * A166589(n) = 7^bigomega(n) * A166589(n) = 7^A001222(n) * A166589(n).