A239672 Product_{i=1..n} J_6(i) where J_6(i) = A069091(i).

1, 63, 45864, 184923648, 2889247076352, 132512427909808128, 15589822118733106642944, 4022922418094840702998413312, 2135013202351949099169693925638144, 2101519115233451721701919767332732796928, 3722967203782973732098252983015976113725767680

Offset: 1

Author

Tom Edgar, Mar 23 2014

Keywords

• nonn

Comments

This is the generalized factorial for A069091.

a(n) is also the determinant of the symmetric n X n matrix M defined by M(i,j) = gcd(i,j)^6 for 1 <= i,j <= n.

References

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

Links

• 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. A069091, A175836, A059381, A059382, A059383.

Programs

Sage

q=15 # change q for more terms
J6=[i^6*prod([1-1/p^6 for p in prime_divisors(i)]) for i in [1..q]]
[prod(J6[0:i+1]) for i in [0..q-1]]