A086134 - OEIS

A086134

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

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

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OFFSET

0,5

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..10000

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

Adjacent sequences: A086131 A086132 A086133 * A086135 A086136 A086137

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 23 2003

STATUS

approved