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A182599
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Number of prime factors of form cn+1 for numbers 7^n+1
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0
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2, 1, 1, 2, 2, 2, 2, 1, 2, 2, 4, 2, 1, 1, 2, 1, 2, 2, 3, 3, 3, 1, 1, 1, 2, 1, 4, 1, 4, 3, 3, 2, 3, 5, 4, 2, 1, 3, 3, 4, 2, 7, 3, 4, 4, 1, 3, 7, 4, 4, 3, 4, 3, 6, 5, 5, 4, 4, 3, 1, 3, 8, 3, 2, 5, 3, 3, 4, 4, 2, 5, 3, 1, 5, 5, 5, 4, 4, 3, 4, 3, 2, 5, 3, 3, 4, 2, 5, 4, 5, 4, 5, 3, 6, 6, 3, 5, 3, 3
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OFFSET
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2,1
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COMMENTS
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Repeated prime factors are counted.
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LINKS
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EXAMPLE
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For n=12, 7^12+1=13841287202=2*73*193*409*1201 has four prime factors of form, namely 73=6n+1, 193=16n+1, 409=34n+1, 1201=100n+1. Thus a(12)=4.
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MATHEMATICA
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m = 7; n = 2; nmax = 100;
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[7^n+1]]; Sum[If[Mod[p[[i]], n]==1, e[[i]], 0], {i, Length[p]}], {n, 2, 50}]
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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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