A167325 Totally multiplicative sequence with a(p) = 6*(p+3) for prime p.

1, 30, 36, 900, 48, 1080, 60, 27000, 1296, 1440, 84, 32400, 96, 1800, 1728, 810000, 120, 38880, 132, 43200, 2160, 2520, 156, 972000, 2304, 2880, 46656, 54000, 192, 51840, 204, 24300000, 3024, 3600, 2880, 1166400, 240, 3960, 3456, 1296000, 264, 64800, 276, 75600

Offset: 1

Author

Jaroslav Krizek, Nov 01 2009

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A001222, A165827, A166591.

Programs

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*6^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (6*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Formula

Multiplicative with a(p^e) = (6*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)+3))^e(k).

a(n) = A165827(n) * A166591(n) = 6^bigomega(n) * A166591(n) = 6^A001222(n) * A166591(n).