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A324977
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Denominator(Bernoulli_{m-1}) / m, where m is the n-th Carmichael number.
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5
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26805565070, 76004922, 702286000198710990, 302278602666, 5360679390, 423023231634556544606744470770, 582934735516230690164248578, 106515855804560422705933720818, 8763422623117673428800595536306232967379299351012370, 9231375124608836430, 94422948020637332890056101961518875879389605546105043450762033482730
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OFFSET
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1,1
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COMMENTS
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a(n) is an integer, because an odd composite number m is a Carmichael number iff m divides the denominator of Bernoulli_{m-1} (by Korselt's criterion and the von Staudt-Clausen theorem). See Pomerance, Selfridge, & Wagstaff, page 1006, and Kellner & Sondow, section on Bernoulli numbers.
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LINKS
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FORMULA
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EXAMPLE
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The 1st Carmichael number is 561, and the denominator of Bernoulli_560 is 15037922004270, so a(1) = 15037922004270 / 561 = 26805565070.
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MAPLE
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with(numtheory): A324977 := proc(n) local C, Fc;
if n = 1 or irem(n, 2) = 0 or isprime(n) then return NULL fi;
Fc := select(isprime, map(i->i+1, divisors(n-1)));
C := mul(i, i=Fc); if irem(C, n) <> 0 then NULL else C/n fi end:
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MATHEMATICA
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carnum = Cases[Range[1, 100000, 2], n_ /; Mod[n, CarmichaelLambda[n]] == 1 && ! PrimeQ[n]];
Table[Denominator[BernoulliB[m - 1]]/m, {m, carnum}]
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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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