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A327033
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N(p-1)/p + D(p-1)/p^2 with p the n-th prime and B(k) = N(k)/D(k) the k-th Bernoulli number.
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2
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0, 1, 1, 1, 1, -37, -211, 2311, 37153, -818946931, 277930363757, -711223555487930419, -6367871182840222481, 35351107998094669831, 12690449182849194963361, -15116334304443206742413679091, 1431925649981017658678758915153153, -19921854762028779869513196624259348280501
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OFFSET
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1,6
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COMMENTS
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a(n) is an integer, as conjectured by Thomas Ordowski and proved by the author in A309132 and A326690.
Ordowski also conjectured that the sequence is a subsequence of A174341.
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LINKS
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EXAMPLE
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Prime(6) = 13 and B(12) = -691/2730, so a(6) = -691/13 + 2730/13^2 = -37.
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MATHEMATICA
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a[n_] := With[{p = Prime[n]}, With[{b = BernoulliB[p - 1]}, (p Numerator[b] + Denominator[b])/p^2]];
Table[a[n], {n, 1, 18}]
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PROG
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(PARI) a(n) = my(p = prime(n), b = bernfrac(p-1)); numerator(b)/p + denominator(b)/p^2; \\ Michel Marcus, Aug 16 2019
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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