A167297 Totally multiplicative sequence with a(p) = 5*(p-2) for prime p.

1, 0, 5, 0, 15, 0, 25, 0, 25, 0, 45, 0, 55, 0, 75, 0, 75, 0, 85, 0, 125, 0, 105, 0, 225, 0, 125, 0, 135, 0, 145, 0, 225, 0, 375, 0, 175, 0, 275, 0, 195, 0, 205, 0, 375, 0, 225, 0, 625, 0, 375, 0, 255, 0, 675, 0, 425, 0, 285, 0, 295, 0, 625, 0, 825, 0, 325, 0, 525

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = (5*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-2))^e(k).

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

a(n) = A165826(n) * A166586(n) = 5^bigomega(n) * A166586(n) = 5^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (5*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165826, A166586.

Sequence in context: A222946 A214121 A024418 * A290867 A027635 A291218

Adjacent sequences: A167294 A167295 A167296 * A167298 A167299 A167300

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved