



5, 266681, 40799043101, 86364397717734821, 36190908596780862323291147613117849902036356128879432564211412588793094572280300268379995976006474252029, 334279880945246012373031736295774418479420559664800307123320901500922509788908032831003901108510816091067151027837158805812525361841612048446489305085140033
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OFFSET

1,1


COMMENTS

A007406[n] are the Wolstenholme numbers: numerator of Sum 1/k^2, k = 1..n. Numbers n such that A007406[n] is prime are listed in A111354[n] = {2,7,13,19,121,188,252,368,605,745,1085,1127,1406,...}.


LINKS

Table of n, a(n) for n=1..6.
Carlos M. da Fonseca, M. Lawrence Glasser, Victor Kowalenko, Generalized cosecant numbers and trigonometric inverse power sums, Applicable Analysis and Discrete Mathematics, Vol. 12, No. 1 (2018), 70109.
Eric Weisstein's World of Mathematics, Harmonic Number.
Eric Weisstein's World of Mathematics, Wolstenholme's Theorem.
Eric Weisstein's World of Mathematics, Wolstenholme Number


FORMULA

a(n) = A007406[ A111354[n] ].


EXAMPLE

A007406[n] begins {1, 5, 49, 205, 5269, 5369, 266681, 1077749, 9778141, ...}.
Thus a(1) = 5 because A007406[2] = 5 is prime but A007406[1] = 1 is not prime.
a(2) = 266681 because A007406[7] = 266681 is prime but all A007406[k] are composite for 2 < k < 7.


MATHEMATICA

Do[f=Numerator[Sum[1/i^2, {i, 1, n}]]; If[PrimeQ[f], Print[{n, f}]], {n, 1, 250}]


CROSSREFS

Cf. A111354, A007406, A001008, A007407, A067567, A056903.
Sequence in context: A038027 A237641 A057679 * A152516 A295532 A240132
Adjacent sequences: A123748 A123749 A123750 * A123752 A123753 A123754


KEYWORD

nonn


AUTHOR

Alexander Adamchuk, Oct 11 2006


STATUS

approved



