A166638 Totally multiplicative sequence with a(p) = 8*(p-1) for prime p.

1, 8, 16, 64, 32, 128, 48, 512, 256, 256, 80, 1024, 96, 384, 512, 4096, 128, 2048, 144, 2048, 768, 640, 176, 8192, 1024, 768, 4096, 3072, 224, 4096, 240, 32768, 1280, 1024, 1536, 16384, 288, 1152, 1536, 16384, 320, 6144, 336, 5120, 8192, 1408, 368, 65536

Offset

1,2

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

Formula

Multiplicative with a(p^e) = (8*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (8*(p(k)-1)^e(k).

a(n) = A165829(n) * A003958(n) = 8^bigomega(n) * A003958(n) = 8^A001222(n) * A003958(n).

Mathematica

DirichletInverse[f_][1] = 1/f[1]; DirichletInverse[f_][n_] :=
DirichletInverse[f][n] = -1/f[1]*Sum[f[n/d]*DirichletInverse[f][d], {d, Most[Divisors[n]]}]; muphi[n_] := MoebiusMu[n]*EulerPhi[n]; a[m_] := DirichletInverse[muphi][m]; Table[a[m]*8^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (8*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)

Crossrefs

Cf. A003958, A001222, A165829.

Sequence in context: A133581 A222544 A307876 * A356961 A339355 A132794

Adjacent sequences: A166635 A166636 A166637 * A166639 A166640 A166641

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved