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A046800
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Number of distinct prime factors of 2^n-1.
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36
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0, 0, 1, 1, 2, 1, 2, 1, 3, 2, 3, 2, 4, 1, 3, 3, 4, 1, 4, 1, 5, 3, 4, 2, 6, 3, 3, 3, 6, 3, 6, 1, 5, 4, 3, 4, 8, 2, 3, 4, 7, 2, 6, 3, 7, 6, 4, 3, 9, 2, 7, 5, 7, 3, 6, 6, 8, 4, 6, 2, 11, 1, 3, 6, 7, 3, 8, 2, 7, 4, 9, 3, 12, 3, 5, 7, 7, 4, 7, 3, 9, 6, 5, 2, 12, 3, 5, 6, 10, 1, 11, 5, 9, 3, 6, 5, 12, 2, 5, 8, 12, 2
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OFFSET
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0,5
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LINKS
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J. Brillhart et al., Factorizations of b^n +- 1. Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.
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FORMULA
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a(n) < 0.7 * n; the constant 0.7 cannot be improved below log 2 using only the size of 2^n-1. - Charles R Greathouse IV, Apr 12 2012
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EXAMPLE
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a(6) = 2 because 63 = 3*3*7 has 2 distinct prime factors.
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MAPLE
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if n <= 1 then
0;
else
numtheory[factorset](2^n-1) ;
nops(%) ;
end if;
end proc:
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MATHEMATICA
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Table[Length[ FactorInteger [ 2^n -1 ] ], {n, 0, 100}]
Join[{0}, PrimeNu/@(2^Range[110]-1)] (* Harvey P. Dale, Mar 09 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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