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%I #6 Mar 24 2014 04:28:24
%S 1,1,2,2,8,16,96,96,192,768,7680,15360,184320,1105920,8847360,8847360,
%T 141557760,283115520,5096079360,20384317440,244611809280,
%U 2446118092800,53814598041600,107629196083200,430516784332800,5166201411993600,10332402823987200
%N Product_{i=1..n} A173557(i).
%C This is the generalized factorial for A173557.
%H Donald E. Knuth and Herbert S. Wilf, <a href="http://www.math.upenn.edu/~wilf/website/dm36.pdf">The power of a prime that divides a generalized binomial coefficient</a>, J. Reine Angew. Math., 396:212-219, 1989.
%F Product_{i=1..n} A173557(i).
%F a(n) = abs(A085542(n)).
%e The first five terms of A173557 are 1,1,2,1,4 so a(5)=4*1*2*1*1=8.
%o (Sage)
%o q=50 # change q for more terms
%o R=[prod([(x-1) for x in prime_divisors(n)]) for n in [1..q]]
%o [prod(R[0:i+1]) for i in [0..q-1]]
%Y Cf. A173557, A085542, A048803.
%K nonn
%O 1,3
%A _Tom Edgar_, Mar 24 2014