A167303 Totally multiplicative sequence with a(p) = 2*(p+2) for prime p.

1, 8, 10, 64, 14, 80, 18, 512, 100, 112, 26, 640, 30, 144, 140, 4096, 38, 800, 42, 896, 180, 208, 50, 5120, 196, 240, 1000, 1152, 62, 1120, 66, 32768, 260, 304, 252, 6400, 78, 336, 300, 7168, 86, 1440, 90, 1664, 1400, 400, 98, 40960, 324, 1568

Offset

1,2

Links

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

Formula

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

a(n) = A061142(n) * A166590(n) = 2^bigomega(n) * A166590(n) = 2^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*2^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (2*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 18 2023 *)

Crossrefs

Cf. A001222, A061142, A166590.

Sequence in context: A060809 A112547 A015657 * A025634 A038288 A230111

Adjacent sequences: A167300 A167301 A167302 * A167304 A167305 A167306

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved