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A082072 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. 6
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
LINKS
FORMULA
a(n) = A020639(A179931(n)). - Antti Karttunen, Nov 03 2017
MATHEMATICA
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 *)
PROG
(PARI) lpf(n)=my(f=factor(n)[, 1]); if(#f, f[1], 1)
a(n)=lpf(gcd(sigma(n), sigma(n, 2))) \\ Charles R Greathouse IV, Feb 14 2013
CROSSREFS
Sequence in context: A072981 A023399 A195476 * A082066 A179931 A130335
KEYWORD
nonn
AUTHOR
Labos Elemer, Apr 07 2003
EXTENSIONS
Name edited by Antti Karttunen after an example by N. J. A. Sloane, Nov 04 2017
STATUS
approved

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Last modified March 28 04:13 EDT 2024. Contains 371235 sequences. (Running on oeis4.)