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A082072
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Smallest prime that divides sigma(n) = A000203(n) and sigma_2(n) = A001157(n), or 1 if sigma(n) and sigma_2(n) are relatively prime.
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6
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1, 1, 2, 7, 2, 2, 2, 5, 13, 2, 2, 2, 2, 2, 2, 31, 2, 13, 2, 2, 2, 2, 2, 2, 31, 2, 2, 2, 2, 2, 2, 3, 2, 2, 2, 7, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 127, 2, 2, 2, 2, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 2, 11, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 7, 2, 2
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OFFSET
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1,3
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LINKS
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FORMULA
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MATHEMATICA
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ffi[x_] := Flatten[FactorInteger[x]]; lf[x_] := Length[FactorInteger[x]]; ba[x_] := Table[Part[ffi[x], 2*w-1], {w, 1, lf[x]}]; f1[x_] := DivisorSigma[1, x]; f2[x_] := DivisorSigma[2, x]; Table[Min[Intersection[ba[f1[w]], ba[f2[w]]]], {w, 1, 128}]
(* Second program: *)
Array[If[CoprimeQ[#1, #2], 1, Min@ Apply[Intersection, Map[FactorInteger[#][[All, 1]] &, {#1, #2}]]] & @@ {DivisorSigma[1, #], DivisorSigma[2, #]} &, 105] (* Michael De Vlieger, Nov 03 2017 *)
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PROG
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(PARI) lpf(n)=my(f=factor(n)[, 1]); if(#f, f[1], 1)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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