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 A182595 Number of prime factors of form cn+1 for numbers 2^n+1 1
 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 3, 1, 1, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 1, 2, 2, 1, 2, 1, 4, 2, 2, 1, 3, 3, 2, 2, 3, 2, 2, 3, 2, 3, 3, 1, 4, 2, 2, 4, 4, 2, 2, 2, 2, 2, 2, 2, 4, 2, 3, 3, 5, 1, 2, 3, 4, 5, 3, 2, 4, 2 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,13 COMMENTS Repeated prime factors are counted. LINKS Seppo Mustonen, Table of n, a(n) for n = 2..250 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=14, 2^n+1=16385=5*29*113 has two prime factors of form, namely 29=2n+1, 113=8n+1. Thus a(14)=2. MATHEMATICA m = 2; n = 2; nmax = 250; 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[2^n+1]]; Sum[If[Mod[p[[i]], n] == 1, e[[i]], 0], {i, Length[p]}], {n, 2, 50}] CROSSREFS Sequence in context: A077479 A335225 A070106 * A109706 A174541 A029444 Adjacent sequences: A182592 A182593 A182594 * A182596 A182597 A182598 KEYWORD nonn AUTHOR Seppo Mustonen, Nov 24 2010 STATUS approved

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Last modified September 23 19:57 EDT 2023. Contains 365554 sequences. (Running on oeis4.)