A059382 Product J_3(i), i=1..n.

1, 7, 182, 10192, 1263808, 230013056, 78664465152, 35241680388096, 24739659632443392, 21474024560960864256, 28560452666077949460480, 41584019081809494414458880, 91318505903653649734151700480, 218616503133346837463559170949120

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)^3 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

• Enrique Pérez Herrero, Table of n, a(n) for n = 1..100
• 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, A059376, A059381, A059383, A059384, A175836.

Programs

Mathematica

JordanTotient[n_, k_:1]:=DivisorSum[n, #^k*MoebiusMu[n/#]&]/; (n>0)&&IntegerQ[n]; A059382[n_]:=Times@@(JordanTotient[#, 3]&/@Range[n]); (* Enrique Pérez Herrero, Aug 06 2011 *)