cp's OEIS Frontend

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

%I A075986 #22 May 08 2023 11:28:04
%S A075986 1,5,49,1261,62689,7629469,1294716361,375074829229,135662633811769,
%T A075986 71859617272521901,60483708554835755641,58166700851687469003901,
%U A075986 79670437976161330893757369,133981073592392620630139873389
%N A075986 Numerator of 1+1/prime(1)^2+ ... + 1/prime(n)^2 where prime(k) is the k-th prime.
%C A075986 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.
%C A075986 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
%D A075986 Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 94-98.
%H A075986 Steven R. Finch, <a href="http://www.people.fas.harvard.edu/~sfinch/constant/hdmrd/hdmrd.html">Meissel-Mertens Constants</a> [Broken link]
%H A075986 Steven R. Finch, <a href="http://web.archive.org/web/20010604201556/http://www.mathsoft.com/asolve/constant/hdmrd/hdmrd.html">Meissel-Mertens Constants</a> [From the Wayback machine]
%F A075986 a(0)=1; a(n)=a(n-1)*prime(n)^2+(prime(1)*...*prime(n-1))^2.
%e A075986 a(2) = 49 so a(3) = 49*p(3)^2 + (2*3)^2 = 49*25 + 36 = 1261.
%t A075986 Table[Det[DiagonalMatrix[Table[Prime[i]^2,{i,1,n}]]+1],{n,1,15}] (* _Alexander Adamchuk_, Jul 08 2006 *)
%t A075986 Accumulate[Join[{1},1/Prime[Range[20]]^2]]//Numerator (* _Harvey P. Dale_, May 08 2023 *)
%Y A075986 Cf. A061015, A075987, A024528.
%K A075986 nonn,frac
%O A075986 0,2
%A A075986 _Zak Seidov_, Sep 28 2002
%E A075986 Edited by _Dean Hickerson_, Sep 30 2002