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A182593
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Number of prime factors of form cn+1 for numbers 6^n-1
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0
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2, 1, 2, 1, 3, 1, 1, 2, 3, 2, 3, 2, 3, 2, 3, 4, 3, 2, 3, 3, 3, 4, 3, 2, 5, 2, 4, 1, 4, 2, 3, 2, 6, 3, 5, 5, 4, 4, 3, 2, 4, 4, 4, 4, 6, 3, 5, 3, 4, 5, 6, 3, 5, 2, 5, 3, 4, 3, 7, 3, 3, 4, 4, 5, 6, 2, 4, 4, 8, 1, 7, 4, 8, 5, 4, 2, 9, 3, 5, 4, 5, 7, 4, 3, 5, 5, 4, 3, 6, 2, 6, 5, 4, 7, 8, 5, 6, 6, 7, 2, 11, 4, 7, 6, 7, 3, 6, 2, 6, 5, 6, 4, 6, 7, 4, 4, 4, 6, 6
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OFFSET
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2,1
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LINKS
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EXAMPLE
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For n=6, 6^n-1=46655=5*7*31*43 and has three prime factors of form cn+1, namely 7=n+1, 31=3n+1, 43=7n+1. Thus a(6)=3.
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MATHEMATICA
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m = 6; n = 2; nmax = 120;
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}]
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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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