cp's OEIS Frontend

A086134 Smallest prime factor of arithmetic derivative of n or a(n)=0 if no such prime exists.

%I A086134 #13 Nov 04 2022 14:42:34
%S A086134 0,0,0,0,2,0,5,0,2,2,7,0,2,0,3,2,2,0,3,0,2,2,13,0,2,2,3,3,2,0,31,0,2,
%T A086134 2,19,2,2,0,3,2,2,0,41,0,2,3,5,0,2,2,3,2,2,0,3,2,2,2,31,0,2,0,3,3,2,2,
%U A086134 61,0,2,2,59,0,2,0,3,5,2,2,71,0,2,2,43,0,2,2,3,2,2,0,3,2,2,2,7,2,2,0,7,3,2,0,7
%N A086134 Smallest prime factor of arithmetic derivative of n or a(n)=0 if no such prime exists.
%H A086134 Alois P. Heinz, <a href="/A086134/b086134.txt">Table of n, a(n) for n = 0..10000</a>
%p A086134 with(numtheory):
%p A086134 d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
%p A086134 a:= n-> (f-> `if`(f<2, 0, min(factorset(f)[])))(d(n)):
%p A086134 seq(a(n), n=0..105);  # _Alois P. Heinz_, Jun 08 2015
%t A086134 d[n_] := n*Sum[i[[2]]/i[[1]], {i, FactorInteger[n]}];
%t A086134 a[n_] := Function[f, If[f<2, 0, Min[FactorInteger[f][[All, 1]]]]][d[n]]; a[0] = 0;
%t A086134 Table[a[n], {n, 0, 105}] (* _Jean-François Alcover_, Mar 23 2017, after _Alois P. Heinz_ *)
%o A086134 (Python)
%o A086134 from sympy import primefactors, factorint
%o A086134 def A086134(n): return 0 if n <= 1 else min(primefactors(m)) if (m:=sum((n*e//p for p,e in factorint(n).items()))) > 1 else 0 # _Chai Wah Wu_, Nov 04 2022
%Y A086134 Cf. A003415.
%K A086134 nonn
%O A086134 0,5
%A A086134 _Labos Elemer_, Jul 23 2003