A167294 Totally multiplicative sequence with a(p) = 2*(p-2) for prime p.

1, 0, 2, 0, 6, 0, 10, 0, 4, 0, 18, 0, 22, 0, 12, 0, 30, 0, 34, 0, 20, 0, 42, 0, 36, 0, 8, 0, 54, 0, 58, 0, 36, 0, 60, 0, 70, 0, 44, 0, 78, 0, 82, 0, 24, 0, 90, 0, 100, 0, 60, 0, 102, 0, 108, 0, 68, 0, 114, 0, 118, 0, 40, 0, 132, 0, 130, 0, 84, 0, 138, 0, 142, 0

Offset

1,3

Links

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

Formula

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

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

a(n) = A061142(n) * A166586(n) = 2^bigomega(n) * A166586(n) = 2^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (2*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A061142, A166586.

Sequence in context: A157195 A019781 A335959 * A304439 A266537 A328337

Adjacent sequences: A167291 A167292 A167293 * A167295 A167296 A167297

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved