A167305 Totally multiplicative sequence with a(p) = 4*(p+2) for prime p.

1, 16, 20, 256, 28, 320, 36, 4096, 400, 448, 52, 5120, 60, 576, 560, 65536, 76, 6400, 84, 7168, 720, 832, 100, 81920, 784, 960, 8000, 9216, 124, 8960, 132, 1048576, 1040, 1216, 1008, 102400, 156, 1344, 1200, 114688, 172, 11520, 180, 13312, 11200, 1600

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (4*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (4*(p(k)+2))^e(k).

a(n) = A165825(n) * A166590(n) = 4^bigomega(n) * A166590(n) = 4^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*4^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (4*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 21 2023 *)

Crossrefs

Cf. A001222, A165825, A166590.

Sequence in context: A103330 A045667 A045658 * A094329 A070573 A186462

Adjacent sequences: A167302 A167303 A167304 * A167306 A167307 A167308

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved