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A089159
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If Mersenne numbers have 3 or more factors, then list the third factor.
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0
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2089, 2099863, 13264529, 20394401, 212885833, 9361973132609, 1113491139767, 65993, 165799, 1654058017289, 110211473, 70084436712553223, 1489459109360039866456940197095433721664951999121, 7648337, 39940132241
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internal format)
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..15.
Chris Caldwell, MersenneNumbers History.
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FORMULA
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A Mersenne number (A001348) is a number of the form 2^p - 1 where p is prime.
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EXAMPLE
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The 10th Mersenne number 2^29 - 1 = 233*1103*2089 and 2089 is the third prime factor. Notice these factors are congruent 1( mod 29 ).
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PROG
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(PARI) mersenne2(n) = { c=0; forprime(x=2, n, c++; y = 2^x-1; f=ifactor(y); if(length(f)>=3, print1(f[3]", "); ) ) } ifactor(n) = \The vector of the integer factors of n with multiplicity. { local(f, j, k, flist); flist=[]; f=Vec(factor(n)); for(j=1, length(f[1]), for(k = 1, f[2][j], flist = concat(flist, f[1][j]) ); ); return(flist) }
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CROSSREFS
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Cf. A016047.
Sequence in context: A106720 A179124 A206606 * A045051 A102504 A270761
Adjacent sequences: A089156 A089157 A089158 * A089160 A089161 A089162
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KEYWORD
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easy,nonn
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AUTHOR
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Cino Hilliard, Dec 06 2003, corrected Nov 16 2006
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STATUS
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approved
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