A167309 Totally multiplicative sequence with a(p) = 8*(p+2) for prime p.

1, 32, 40, 1024, 56, 1280, 72, 32768, 1600, 1792, 104, 40960, 120, 2304, 2240, 1048576, 152, 51200, 168, 57344, 2880, 3328, 200, 1310720, 3136, 3840, 64000, 73728, 248, 71680, 264, 33554432, 4160, 4864, 4032, 1638400, 312, 5376, 4800, 1835008, 344, 92160, 360

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (8*(p+2))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)+2))^e(k).

a(n) = A165829(n) * A166590(n) = 8^bigomega(n) * A166590(n) = 8^A001222(n) * A166590(n).

Mathematica

a[1] = 1; a[n_] := (fi = FactorInteger[n]; Times @@ ((fi[[All, 1]] + 2)^fi[[All, 2]])); Table[a[n]*8^PrimeOmega[n], {n, 1, 100}] (* G. C. Greubel, Jun 07 2016 *)
f[p_, e_] := (8*(p+2))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 19 2023 *)

Crossrefs

Cf. A001222, A165829, A166590.

Sequence in context: A326112 A363530 A240246 * A159007 A114042 A302168

Adjacent sequences: A167306 A167307 A167308 * A167310 A167311 A167312

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Nov 01 2009

Status

approved