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5, 266681, 40799043101, 86364397717734821, 36190908596780862323291147613117849902036356128879432564211412588793094572280300268379995976006474252029, 334279880945246012373031736295774418479420559664800307123320901500922509788908032831003901108510816091067151027837158805812525361841612048446489305085140033
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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1,1
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COMMENTS
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A007406 lists the Wolstenholme numbers.
Numbers k such that A007406(k) is prime are listed in A111354.
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LINKS
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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), 70-109.
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
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FORMULA
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a(n) = A007406(A111354(n)).
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EXAMPLE
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A007406 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.
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MATHEMATICA
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Do[f=Numerator[Sum[1/i^2, {i, 1, n}]]; If[PrimeQ[f], Print[{n, f}]], {n, 1, 250}]
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CROSSREFS
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Cf. A111354, A007406, A001008, A007407, A067567, A056903.
Sequence in context: A038027 A237641 A057679 * A152516 A295532 A240132
Adjacent sequences: A123748 A123749 A123750 * A123752 A123753 A123754
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KEYWORD
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nonn
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AUTHOR
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Alexander Adamchuk, Oct 11 2006
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STATUS
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approved
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