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%I #6 Dec 05 2013 19:57:02
%S 0,0,0,1,0,11,0,180,380,1627,0,379692,0,39168360,19495784,109797856,0,
%T 1247559689920,0,339677685789414,39530054317464,80449141757760,0,
%U 49078434999009645846,4049791363412815104,2006460609738963840
%N For each k from 0 through n-1, take the largest value of C(n,r) that divides k! and sum k! / C(n,r) for all cases where C(n,r)>1.
%C a(p) = 0, iff p is a prime. This is a generalization of sequence A110416.
%e a(6) = 3!/(C(6,1)) + 4!/(C(6,1)) + 5!/(C(6,3)) = 1 + 4 + 6 = 11.
%o ;;PLT DrScheme. (Zucker)
%o ;;(! n), (binom n r) have the obvious definitions
%o ;;(min-list a-list) produces 0 if the list is empty.
%o (define (A110417 n)
%o (local ((define (smallest-C-n-r-quotient kfactorial)
%o (min-list (filter integer?
%o (build-list (quotient n 2)
%o (lambda (r) (/ kfactorial (binom n (add1 r)))))))))
%o (apply + (build-list n (lambda (k) (smallest-C-n-r-quotient (! k)))))))
%Y Cf. A110416.
%K easy,nonn
%O 1,6
%A _Amarnath Murthy_, Aug 01 2005
%E Corrected and extended by _Joshua Zucker_, May 10 2006
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