A166635 Totally multiplicative sequence with a(p) = 5*(p-1) for prime p.

1, 5, 10, 25, 20, 50, 30, 125, 100, 100, 50, 250, 60, 150, 200, 625, 80, 500, 90, 500, 300, 250, 110, 1250, 400, 300, 1000, 750, 140, 1000, 150, 3125, 500, 400, 600, 2500, 180, 450, 600, 2500, 200, 1500, 210, 1250, 2000, 550, 230, 6250, 900, 2000

Offset: 1

Author

Jaroslav Krizek, Oct 18 2009

Keywords

• nonn
• easy
• mult

Links

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

Crossrefs

Cf. A001222, A003958, A165826, A166633, A166634.

Programs

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]*5^(PrimeOmega[m]), {m, 1, 100}] (* G. C. Greubel, May 20 2016 *)
a[p_?PrimeQ] := a[p] = 5*(p-1); a[1] = 1; a[n_] := ({pp, ee} = FactorInteger[n] // Transpose; Times @@ ((a /@ pp)^ee)); Array[a, 50] (* Jean-François Alcover, Feb 02 2018 *)

Formula

Multiplicative with a(p^e) = (5*(p-1))^e. If n = Product p(k)^e(k) then a(n) = Product (5*(p(k)-1))^e(k).

a(n) = A165826(n) * A003958(n) = 5^bigomega(n) * A003958(n) = 5^A001222(n) * A003958(n).