A327033 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.

0, 1, 1, 1, 1, -37, -211, 2311, 37153, -818946931, 277930363757, -711223555487930419, -6367871182840222481, 35351107998094669831, 12690449182849194963361, -15116334304443206742413679091, 1431925649981017658678758915153153, -19921854762028779869513196624259348280501

Offset: 1

Author

Jonathan Sondow, Aug 15 2019

Keywords

• sign

Comments

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.

Examples

			Prime(6) = 13 and B(12) = -691/2730, so a(6) = -691/13 + 2730/13^2 = -37.
		

Links

• Wikipedia, Bernoulli number

Crossrefs

Cf. A174341, A309132, A326690.

Programs

Mathematica

a[n_] := With[{p = Prime[n]}, With[{b = BernoulliB[p - 1]}, (p  Numerator[b] + Denominator[b])/p^2]];
Table[a[n], {n, 1, 18}]

PARI

a(n) = my(p = prime(n), b = bernfrac(p-1)); numerator(b)/p + denominator(b)/p^2; \\ Michel Marcus, Aug 16 2019