A167299 Totally multiplicative sequence with a(p) = 7*(p-2) for prime p.

1, 0, 7, 0, 21, 0, 35, 0, 49, 0, 63, 0, 77, 0, 147, 0, 105, 0, 119, 0, 245, 0, 147, 0, 441, 0, 343, 0, 189, 0, 203, 0, 441, 0, 735, 0, 245, 0, 539, 0, 273, 0, 287, 0, 1029, 0, 315, 0, 1225, 0, 735, 0, 357, 0, 1323, 0, 833, 0, 399, 0, 413, 0, 1715, 0, 1617, 0, 455

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = (7*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)-2))^e(k).

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

a(n) = A165828(n) * A166586(n) = 7^bigomega(n) * A166586(n) = 7^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*7^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (7*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165828, A166586.

Sequence in context: A067152 A052440 A246919 * A340952 A282071 A064854

Adjacent sequences: A167296 A167297 A167298 * A167300 A167301 A167302

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved