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A086134
Smallest prime factor of arithmetic derivative of n or a(n)=0 if no such prime exists.
5
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, 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, 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
OFFSET
0,5
LINKS
MAPLE
with(numtheory):
d:= n-> n*add(i[2]/i[1], i=ifactors(n)[2]):
a:= n-> (f-> `if`(f<2, 0, min(factorset(f)[])))(d(n)):
seq(a(n), n=0..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, Min[FactorInteger[f][[All, 1]]]]][d[n]]; a[0] = 0;
Table[a[n], {n, 0, 105}] (* Jean-François Alcover, Mar 23 2017, after Alois P. Heinz *)
PROG
(Python)
from sympy import primefactors, factorint
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
CROSSREFS
Cf. A003415.
Sequence in context: A145962 A066442 A171388 * A071090 A105221 A215339
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 23 2003
STATUS
approved