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

0,2

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

References

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

Links

Table of n, a(n) for n=0..13.

Steven R. Finch, Meissel-Mertens Constants [Broken link]

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

Formula

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

Example

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

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 *)

Crossrefs

Cf. A061015, A075987, A024528.

Sequence in context: A363480 A193199 A224680 * A251657 A084765 A203411

Adjacent sequences: A075983 A075984 A075985 * A075987 A075988 A075989

Keyword

nonn,frac

Author

Zak Seidov, Sep 28 2002

Extensions

Edited by Dean Hickerson, Sep 30 2002

Status

approved