A059383 Product J_4(i), i=1..n.

1, 15, 1200, 288000, 179712000, 215654400000, 517570560000000, 1987470950400000000, 12878811758592000000000, 120545678060421120000000000, 1764788726804565196800000000000, 33883943554647651778560000000000000, 967725427920736934795673600000000000000

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)^4 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..140
• 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, A059377, A059381, A059382, A059383, A059384, A175836.

Programs

Mathematica

JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/#]&]/; (n>0)&&IntegerQ[n]; A059383[n_]:=Times@@(JordanTotient[#, 4]&/@Range[n]); (* Enrique Pérez Herrero, Aug 12 2011 *)