OFFSET
2,1
COMMENTS
For n>1, a(n) is the absolute value of the numerator of the determinant of the n X n matrix with elements M[i,j] = 1/(prime(i)-1)^2 for i=j and 1 otherwise. - Alexander Adamchuk, Jun 02 2006
REFERENCES
Steven R. Finch, Mathematical Constants, Cambridge, 2003, pp. 84-94.
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, ch. 22.20
LINKS
Steven R. Finch, Hardy-Littlewood Constants [Broken link]
Steven R. Finch, Hardy-Littlewood Constants [From the Wayback machine]
FORMULA
a(n) = a(n-1)*(prime(n)*(prime(n)-2)) / gcd(a(n-1)*prime(n)*(prime(n)-2), A062271(n)) for n > 2.
EXAMPLE
a(4) = 175 = 3*1*5*3*7*5 / gcd(3*1*5*3*7*5, 2*2*4*4*6*6).
MATHEMATICA
Numerator[Abs[Table[ Det[ DiagonalMatrix[ Table[ 1/(Prime[i]-1)^2 - 1, {i, 1, n} ] ] + 1 ], {n, 2, 20} ]]] (* Alexander Adamchuk, Jun 02 2006 *)
PROG
(PARI) a(n) = numerator(prod(k=2, n, 1-1/(prime(k)-1)^2)); \\ Michel Marcus, May 31 2022
CROSSREFS
KEYWORD
easy,nonn,frac
AUTHOR
Frank Ellermann, Jun 16 2001
EXTENSIONS
Typo in link corrected by Martin Griffiths, Apr 03 2009
STATUS
approved