A166636 Totally multiplicative sequence with a(p) = 6*(p-1) for prime p.

1, 6, 12, 36, 24, 72, 36, 216, 144, 144, 60, 432, 72, 216, 288, 1296, 96, 864, 108, 864, 432, 360, 132, 2592, 576, 432, 1728, 1296, 168, 1728, 180, 7776, 720, 576, 864, 5184, 216, 648, 864, 5184, 240, 2592, 252, 2160, 3456, 792, 276, 15552, 1296, 3456

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (6*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (6*(p(k)-1)^e(k).

a(n) = A165827(n) * A003958(n) = 6^bigomega(n) * A003958(n) = 6^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]*6^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (6*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)

Crossrefs

Cf. A001222, A003958, A165827.

Sequence in context: A196992 A321839 A192029 * A167338 A078402 A127845

Adjacent sequences: A166633 A166634 A166635 * A166637 A166638 A166639

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved