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)*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
KEYWORD
nonn,frac
AUTHOR
Zak Seidov, Sep 28 2002
EXTENSIONS
Edited by Dean Hickerson, Sep 30 2002
STATUS
approved