A167306 Totally multiplicative sequence with a(p) = 5*(p+2) for prime p.

1, 20, 25, 400, 35, 500, 45, 8000, 625, 700, 65, 10000, 75, 900, 875, 160000, 95, 12500, 105, 14000, 1125, 1300, 125, 200000, 1225, 1500, 15625, 18000, 155, 17500, 165, 3200000, 1625, 1900, 1575, 250000, 195, 2100, 1875, 280000, 215, 22500, 225, 26000

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (5*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)+2))^e(k).

a(n) = A165826(n) * A166590(n) = 5^bigomega(n) * A166590(n) = 5^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*5^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (5*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165826, A166590.

Sequence in context: A295152 A292199 A269308 * A061840 A252660 A265401

Adjacent sequences: A167303 A167304 A167305 * A167307 A167308 A167309

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved