A166641 Totally multiplicative sequence with a(p) = 10*(p-1) for prime p.

1, 10, 20, 100, 40, 200, 60, 1000, 400, 400, 100, 2000, 120, 600, 800, 10000, 160, 4000, 180, 4000, 1200, 1000, 220, 20000, 1600, 1200, 8000, 6000, 280, 8000, 300, 100000, 2000, 1600, 2400, 40000, 360, 1800, 2400, 40000, 400, 12000, 420, 10000, 16000

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = (10*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (10*(p(k)-1)^e(k).

a(n) = A165831(n) * A003958(n) = 10^bigomega(n) * A003958(n) = 10^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]*10^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
f[p_, e_] := (10*(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] = 10*(f[k, 1]-1)); factorback(f); } \\ Michel Marcus, May 21 2016

Crossrefs

Cf. A001222, A003958, A165831.

Sequence in context: A276764 A215878 A200985 * A101244 A260743 A161999

Adjacent sequences: A166638 A166639 A166640 * A166642 A166643 A166644

Keyword

nonn,easy,mult

Author

Jaroslav Krizek, Oct 18 2009

Status

approved