A075986 Numerator of 1+1/prime(1)^2+ ... + 1/prime(n)^2 where prime(k) is the k-th prime.

1, 5, 49, 1261, 62689, 7629469, 1294716361, 375074829229, 135662633811769, 71859617272521901, 60483708554835755641, 58166700851687469003901, 79670437976161330893757369, 133981073592392620630139873389

Offset: 0

Author

Zak Seidov, Sep 28 2002

Keywords

• nonn
• frac

Comments

The sum is similar to that in A061015 with an additional 1. The sum in the definition has limit about 1.45224742. The case of reciprocal cubes is in A075987.

For n>0 a(n) is the determinant of the n X n matrix with elements M[i,j] = 1+Prime[i]^2 if i=j and 1 otherwise. - Alexander Adamchuk, Jul 08 2006

Examples

			a(2) = 49 so a(3) = 49*p(3)^2 + (2*3)^2 = 49*25 + 36 = 1261.
		

References

• Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 94-98.

Links

• Steven R. Finch, Meissel-Mertens Constants [Broken link]
• Steven R. Finch, Meissel-Mertens Constants [From the Wayback machine]

Crossrefs

Cf. A061015, A075987, A024528.

Programs

Mathematica

Table[Det[DiagonalMatrix[Table[Prime[i]^2,{i,1,n}]]+1],{n,1,15}] (* Alexander Adamchuk, Jul 08 2006 *)
Accumulate[Join[{1},1/Prime[Range[20]]^2]]//Numerator (* Harvey P. Dale, May 08 2023 *)

Formula

a(0)=1; a(n)=a(n-1)*prime(n)^2+(prime(1)*...*prime(n-1))^2.

Extensions

Edited by Dean Hickerson, Sep 30 2002