A167326 Totally multiplicative sequence with a(p) = 7*(p+3) for prime p.

1, 35, 42, 1225, 56, 1470, 70, 42875, 1764, 1960, 98, 51450, 112, 2450, 2352, 1500625, 140, 61740, 154, 68600, 2940, 3430, 182, 1800750, 3136, 3920, 74088, 85750, 224, 82320, 238, 52521875, 4116, 4900, 3920, 2160900, 280, 5390, 4704, 2401000, 308

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (7*(p+3))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)+3))^e(k).

a(n) = A165828(n) * A166591(n) = 7^bigomega(n) * A166591(n) = 7^A001222(n) * A166591(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 3)^fi[[All, 2]])); Table[a[n]*7^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 09 2016 *)
f[p_, e_] := (7*(p+3))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165828, A166591.

Sequence in context: A141741 A122755 A298156 * A141638 A033857 A110264

Adjacent sequences: A167323 A167324 A167325 * A167327 A167328 A167329

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved