A167324 Totally multiplicative sequence with a(p) = 5*(p+3) for prime p.

1, 25, 30, 625, 40, 750, 50, 15625, 900, 1000, 70, 18750, 80, 1250, 1200, 390625, 100, 22500, 110, 25000, 1500, 1750, 130, 468750, 1600, 2000, 27000, 31250, 160, 30000, 170, 9765625, 2100, 2500, 2000, 562500, 200, 2750, 2400, 625000, 220, 37500, 230

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (5*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+3))^e(k).

a(n) = A165826(n) * A166591(n) = 5^bigomega(n) * A166591(n) = 5^A001222(n) * A166591(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (5*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 22 2023 *)

Crossrefs

Cf. A001222, A165826, A166591.

Sequence in context: A161835 A284045 A213929 * A307283 A184042 A157646

Adjacent sequences: A167321 A167322 A167323 * A167325 A167326 A167327

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved