A086131 Largest prime factor of arithmetic derivative of n if it exists, or a(n)=0 for n=1 and n=prime.

0, 0, 0, 2, 0, 5, 0, 3, 3, 7, 0, 2, 0, 3, 2, 2, 0, 7, 0, 3, 5, 13, 0, 11, 5, 5, 3, 2, 0, 31, 0, 5, 7, 19, 3, 5, 0, 7, 2, 17, 0, 41, 0, 3, 13, 5, 0, 7, 7, 5, 5, 7, 0, 3, 2, 23, 11, 31, 0, 23, 0, 11, 17, 3, 3, 61, 0, 3, 13, 59, 0, 13, 0, 13, 11, 5, 3, 71, 0, 11, 3, 43, 0, 31, 11, 5, 2, 7, 0, 41, 5, 3

Offset: 1

Author

Labos Elemer, Jul 23 2003

Keywords

• nonn

Links

• Floris P. van Doorn and Jasper Mulder, Table of n, a(n) for n = 1..20000

Crossrefs

Cf. A003415.

Programs

Maple

with(numtheory):
d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
a:= n-> (f-> `if`(f<2, 0, max(factorset(f)[])))(d(n)):
seq(a(n), n=1..105);  # Alois P. Heinz, Jun 08 2015

Mathematica

d[n_] := n*Sum[i[[2]]/i[[1]], {i, FactorInteger[n]}];
a[n_] := Function[f, If[f<2, 0, Max[FactorInteger[f][[All, 1]]]]][d[n]];
Table[a[n], {n, 1, 105}] (* Jean-François Alcover, Mar 23 2017, after Alois P. Heinz *)