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A182594
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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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1, 1, 2, 1, 2, 2, 1, 3, 3, 2, 2, 1, 4, 2, 3, 2, 4, 2, 3, 1, 4, 3, 4, 3, 3, 4, 4, 3, 3, 3, 2, 4, 3, 3, 3, 3, 4, 4, 5, 3, 4, 2, 4, 2, 4, 2, 3, 4, 4, 5, 5, 3, 5, 1, 6, 3, 4, 4, 5, 4, 6, 2, 3, 6, 6, 4, 6, 3, 8, 2, 5, 5, 5, 3, 2, 3, 7, 2, 5
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OFFSET
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2,3
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LINKS
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EXAMPLE
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For n=9, 7^n-1=40353606=2*3^3*19*37*1063 has three prime factors of form, namely 19=2n+1, 37=6n+1, 1063=118n+1. Thus a(9)=3.
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MATHEMATICA
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m = 7; n = 2; nmax = 80;
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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