A059384 a(n) = Product_{i=1..n} J_5(i).

1, 31, 7502, 7441984, 23248758016, 174412182636032, 2931171141381153792, 93047096712003345973248, 5471727569246068763302821888, 529903984716066283313298482921472, 85341036738522474927606720674503065600, 20487310643596659421020979792003903940198400

Offset: 1

Author

N. J. A. Sloane, Jan 28 2001

Keywords

• nonn

Comments

a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(i,j)^5 for 1 <= i,j <= n. - Avi Peretz (njk(AT)netvision.net.il), Mar 22 2001

References

• L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 203, #17.

Links

• G. C. Greubel, Table of n, a(n) for n = 1..120
• Antal Bege, Hadamard product of GCD matrices, Acta Univ. Sapientiae, Mathematica, 1, 1 (2009) 43-49.
• Eric Weisstein's World of Mathematics, Le Paige's Theorem

Crossrefs

Cf. A001088, A059378, A059381, A059382, A059383, A175836.

Programs

Mathematica

JordanTotient[n_Integer, k_: 1] := DivisorSum[n, #^k*MoebiusMu[n/#] &];  f[n_] := Times @@ (JordanTotient[#, 5] & /@ Range[n]); (* Enrique Pérez Herrero *)  Array[f, 11] (* Robert G. Wilson v, Oct 08 2011 *)