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 A182596 Number of prime factors of form cn+1 for numbers 3^n+1 0
 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 1, 1, 2, 3, 1, 3, 2, 2, 2, 3, 2, 1, 4, 2, 2, 2, 2, 3, 1, 2, 1, 4, 2, 1, 2, 3, 2, 5, 2, 2, 2, 1, 3, 3, 2, 3, 2, 2, 3, 6, 2, 2, 2, 3, 3, 5, 2, 2, 5, 2, 3, 5, 1, 2, 1, 2, 3, 6, 3, 5, 3, 2, 3, 6, 4, 1, 2, 3, 4, 7, 3, 4, 5, 4, 5, 8, 3, 3, 3, 6, 2, 6, 2, 4, 4, 3, 5, 6, 3, 2, 5, 3, 4, 6, 4, 3, 7, 4, 4, 7, 7, 3, 4, 3, 3, 6, 1, 2, 5, 4, 4, 6, 2, 3, 4, 4, 5, 6, 3 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,7 COMMENTS Repeated prime factors are counted. LINKS Table of n, a(n) for n=2..130. S. Mustonen, On prime factors of numbers m^n+-1 Seppo Mustonen, On prime factors of numbers m^n+-1 [Local copy] EXAMPLE For n=8, 3^n+1=6562=2*17*193 has two prime factors of form, namely 17=2n+1, 193=24n+1. Thus a(8)=2. MATHEMATICA m = 3; n = 2; nmax = 130; While[n <= nmax, {l = FactorInteger[m^n + 1]; s = 0; For[i = 1, i <= Length[l], i++, {p = l[[i, 1]]; If[IntegerQ[(p - 1)/n] == True, s = s + l[[i, 2]]]; }]; a[n] = s; } n++; ]; Table[a[n], {n, 2, nmax}] Table[{p, e}=Transpose[FactorInteger[3^n+1]]; Sum[If[Mod[p[[i]], n] == 1, e[[i]], 0], {i, Length[p]}], {n, 2, 50}] CROSSREFS Sequence in context: A164002 A322156 A332278 * A087775 A366091 A089955 Adjacent sequences: A182593 A182594 A182595 * A182597 A182598 A182599 KEYWORD nonn AUTHOR Seppo Mustonen, Nov 24 2010 STATUS approved

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Last modified December 7 11:41 EST 2023. Contains 367656 sequences. (Running on oeis4.)