A123751 Primes in A007406.

5, 266681, 40799043101, 86364397717734821, 36190908596780862323291147613117849902036356128879432564211412588793094572280300268379995976006474252029, 334279880945246012373031736295774418479420559664800307123320901500922509788908032831003901108510816091067151027837158805812525361841612048446489305085140033

Offset: 1

Author

Alexander Adamchuk, Oct 11 2006

Keywords

• nonn

Comments

A007406 lists the Wolstenholme numbers.

Numbers k such that A007406(k) is prime are listed in A111354.

Examples

			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.
		

Links

• 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

Crossrefs

Cf. A111354, A007406, A001008, A007407, A067567, A056903.

Programs

Mathematica

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

Formula

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