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A309235
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Composite numbers m such that A309132(m) <= m.
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4
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561, 1105, 1729, 2465, 2821, 5005, 6601, 8911, 10585, 15841, 28405, 29341, 41041, 46657, 47125, 52633, 62745, 63973, 75361, 98605, 101101
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OFFSET
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1,1
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COMMENTS
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It contains all the Carmichael numbers A002997 and the numbers 5005, 28405, 47125, 98605, ...
Carmichael numbers m for which A309132(m) < m are 561, 1105, 46657, 52633, ...
If m is a Carmichael number, then not only is A309132(m) <= m, but in fact A309132(m) | m. (Proof. As m is a Carmichael number, m | D(m-1) where B(k) = N(k)/D(k) is the k-th Bernoulli number. So I := N(m-1) + D(m-1)/m is an integer. Hence A309132(m) = Denominator(I/m) is a divisor of m.) - Jonathan Sondow, Jul 17 2019
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LINKS
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MATHEMATICA
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f[n_] := Denominator[Numerator[BernoulliB[n - 1]] / n + Denominator[BernoulliB[n - 1]] / n^2]; Select[Range[10^4], CompositeQ[#] && f[#] <= # &]
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PROG
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(PARI) f(n) = my(b=bernfrac(n-1)); denominator(numerator(b)/n + denominator(b)/n^2); \\ A309132
isok(n) = (n>1) && !isprime(n) && (f(n) <= n); \\ Michel Marcus, Jul 17 2019
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CROSSREFS
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KEYWORD
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nonn,hard,more
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AUTHOR
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STATUS
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approved
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