A167331 Totally multiplicative sequence with a(p) = 2*(3p-1) = 6p-2 for prime p.

1, 10, 16, 100, 28, 160, 40, 1000, 256, 280, 64, 1600, 76, 400, 448, 10000, 100, 2560, 112, 2800, 640, 640, 136, 16000, 784, 760, 4096, 4000, 172, 4480, 184, 100000, 1024, 1000, 1120, 25600, 220, 1120, 1216, 28000, 244, 6400, 256, 6400, 7168, 1360, 280

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (2*(3p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (2*(3*p(k)-1))^e(k).

a(n) = A061142(n) * A166652(n) = 2^bigomega(n) * A166652(n) = 2^A001222(n) * A166652(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((3*fi[[All, 1]] - 1)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 06 2016 *)
f[p_, e_] := (6*p-2)^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Prog

(PARI) a(n) = {my(f=factor(n)); for (k=1, #f~, f[k, 1] = 6*f[k, 1]-2; ); factorback(f); } \\ Michel Marcus, Jun 06 2016

Crossrefs

Cf. A001222, A061142, A166652.

Sequence in context: A033460 A056848 A219854 * A255531 A157159 A176664

Adjacent sequences: A167328 A167329 A167330 * A167332 A167333 A167334

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved