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A239672 Product_{i=1..n} J_6(i) where J_6(i) = A069091(i). 1
1, 63, 45864, 184923648, 2889247076352, 132512427909808128, 15589822118733106642944, 4022922418094840702998413312, 2135013202351949099169693925638144, 2101519115233451721701919767332732796928, 3722967203782973732098252983015976113725767680 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..11.

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

Cf. A069091, A175836, A059381, A059382, A059383.

Sequence in context: A210824 A110852 A212859 * A136677 A135812 A069452

Adjacent sequences:  A239669 A239670 A239671 * A239673 A239674 A239675

KEYWORD

nonn

AUTHOR

Tom Edgar, Mar 23 2014

STATUS

approved

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Last modified September 29 10:06 EDT 2020. Contains 337428 sequences. (Running on oeis4.)