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 A075986 Numerator of 1+1/p(1)^2+ ... + 1/p(n)^2 where p(k) = k-th prime. 6
 1, 5, 49, 1261, 62689, 7629469, 1294716361, 375074829229, 135662633811769, 71859617272521901, 60483708554835755641, 58166700851687469003901, 79670437976161330893757369, 133981073592392620630139873389 (list; graph; refs; listen; history; text; internal format)
 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 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)*p(n)^2+(p(1)*...*p(n-1))^2. a(n) = Det[DiagonalMatrix[Table[Prime[i]^2,{i,1,n}]]+1] for n>0. - Alexander Adamchuk, Jul 08 2006 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 CROSSREFS Cf. A061015, A075987, A024528. Sequence in context: A249588 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

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Last modified May 8 19:28 EDT 2021. Contains 343666 sequences. (Running on oeis4.)