A167301 Totally multiplicative sequence with a(p) = 9*(p-2) for prime p.

1, 0, 9, 0, 27, 0, 45, 0, 81, 0, 81, 0, 99, 0, 243, 0, 135, 0, 153, 0, 405, 0, 189, 0, 729, 0, 729, 0, 243, 0, 261, 0, 729, 0, 1215, 0, 315, 0, 891, 0, 351, 0, 369, 0, 2187, 0, 405, 0, 2025, 0, 1215, 0, 459, 0, 2187, 0, 1377, 0, 513, 0, 531, 0, 3645, 0, 2673, 0

Offset

1,3

Links

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

Formula

Multiplicative with a(p^e) = (9*(p-2))^e. If n = Product p(k)^e(k) then a(n) = Product (9*(p(k)-2))^e(k).

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

a(n) = A165830(n) * A166586(n) = 9^bigomega(n) * A166586(n) = 9^A001222(n) * A166586(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] - 2)^fi[[All, 2]])); Table[a[n]*9^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (9*(p-2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165830, A166586.

Sequence in context: A167354 A005066 A076262 * A177741 A182213 A340954

Adjacent sequences: A167298 A167299 A167300 * A167302 A167303 A167304

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved