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A166635
Totally multiplicative sequence with a(p) = 5*(p-1) for prime p.
1
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
1,2
LINKS
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).
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 *)
CROSSREFS
KEYWORD
nonn,mult
AUTHOR
Jaroslav Krizek, Oct 18 2009
STATUS
approved