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A086134
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Smallest prime factor of arithmetic derivative of n or a(n)=0 if no such prime exists.
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5
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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
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0,5
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LINKS
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MAPLE
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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)):
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MATHEMATICA
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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;
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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