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A027762
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Denominator of Sum_{p prime, p-1 divides 2*n} 1/p.
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8
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6, 30, 42, 30, 66, 2730, 6, 510, 798, 330, 138, 2730, 6, 870, 14322, 510, 6, 1919190, 6, 13530, 1806, 690, 282, 46410, 66, 1590, 798, 870, 354, 56786730, 6, 510, 64722, 30, 4686, 140100870, 6, 30, 3318, 230010, 498, 3404310, 6, 61410, 272118, 1410, 6, 4501770
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OFFSET
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1,1
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COMMENTS
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From the von Staudt-Clausen theorem, denominator(B_2n) = product of primes p such that (p-1)|2n.
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REFERENCES
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G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Th. 118.
H. Rademacher, Topics in Analytic Number Theory, Springer, 1973, Chap. 1.
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LINKS
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FORMULA
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PROG
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(PARI)
a(n)=
{
my(s=0);
forprime (p=2, 2*n+1, if( (2*n)%(p-1)==0, s+=1/p ) );
return( denominator(s) );
}
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CROSSREFS
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KEYWORD
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nonn,frac
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AUTHOR
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STATUS
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approved
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