A166637 Totally multiplicative sequence with a(p) = 7*(p-1) for prime p.

1, 7, 14, 49, 28, 98, 42, 343, 196, 196, 70, 686, 84, 294, 392, 2401, 112, 1372, 126, 1372, 588, 490, 154, 4802, 784, 588, 2744, 2058, 196, 2744, 210, 16807, 980, 784, 1176, 9604, 252, 882, 1176, 9604, 280, 4116, 294, 3430, 5488, 1078, 322, 33614, 1764

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (7*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (7*(p(k)-1)^e(k).

a(n) = A165828(n) * A003958(n) = 7^bigomega(n) * A003958(n) = 7^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]*7^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (7*(p-1))^e; a[1] = 1; a[n_] := Times @@ f @@@ FactorInteger[n]; Array[a, 100] (* Amiram Eldar, Oct 17 2023 *)

Prog

(PARI) a(n) = {my(f = factor(n)); for (k=1, #f~, f[k, 1] = 7*(f[k, 1]-1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003958, A165828.

Sequence in context: A098328 A062098 A045759 * A237686 A170918 A033650

Adjacent sequences: A166634 A166635 A166636 * A166638 A166639 A166640

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved