login
A239672
Product_{i=1..n} J_6(i) where J_6(i) = A069091(i).
2
1, 63, 45864, 184923648, 2889247076352, 132512427909808128, 15589822118733106642944, 4022922418094840702998413312, 2135013202351949099169693925638144, 2101519115233451721701919767332732796928, 3722967203782973732098252983015976113725767680
OFFSET
1,2
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
PROG
(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]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Tom Edgar, Mar 23 2014
STATUS
approved