A167308 Totally multiplicative sequence with a(p) = 7*(p+2) for prime p.

1, 28, 35, 784, 49, 980, 63, 21952, 1225, 1372, 91, 27440, 105, 1764, 1715, 614656, 133, 34300, 147, 38416, 2205, 2548, 175, 768320, 2401, 2940, 42875, 49392, 217, 48020, 231, 17210368, 3185, 3724, 3087, 960400, 273, 4116, 3675, 1075648, 301, 61740, 315, 71344

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (7*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)+2))^e(k).

a(n) = A165828(n) * A166590(n) = 7^bigomega(n) * A166590(n) = 7^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*7^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (7*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165828, A166590.

Sequence in context: A039347 A043170 A043950 * A303261 A168106 A061900

Adjacent sequences: A167305 A167306 A167307 * A167309 A167310 A167311

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved