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%I #12 Feb 08 2023 17:38:19
%S 10,0,105,2240,1512,0,660,0,617760,16016,225225,0,495040,0,69768,
%T 18604800,639967910400,0,8855,284680230912,1245476010240000,
%U 41993952000,159845400,0,475020,0,9939793500,156068011008000
%N a(n) = A092914(n)/n = the least integer value of (n-1)!/(n*k!).
%C From _Robert Israel_, Jun 26 2020: (Start)
%C If n is prime, (n-1)!/n is not an integer and a(n) is taken to be 0.
%C If n = 2*p where p is an odd prime, a(n) = (2*p-1)!/(2*p!). (End)
%H Robert Israel, <a href="/A092916/b092916.txt">Table of n, a(n) for n = 6..733</a>
%e a(9) = 20160/9 = 2240.
%p f:= proc(n) local t,v,k;
%p if isprime(n) then return 0 fi;
%p t:= (n-1)!/n;
%p for k from 1 do
%p v:= t/k;
%p if not v::integer then return t fi;
%p t:= v;
%p od
%p end proc:
%p map(f, [$6..40]); # _Robert Israel_, Jun 26 2020
%t a[n_] := Module[{P, r}, For[r = 1, True, r++, P = (n-r)* Pochhammer[n-r+1, r]/n; If[Divisible[P, n], Return[P/n]]]];
%t Table[a[n], {n, 6, 40}] (* _Jean-François Alcover_, Feb 07 2023 *)
%o (PARI) m=34;for(n=6,m,r=1;p=n-r;while(r<=n&&p%n>0,r++;p=p*(n-r));print1(p/n,","))
%Y Cf. A092914, A092915.
%K nonn,look
%O 6,1
%A _Amarnath Murthy_, Mar 16 2004
%E More terms from _Klaus Brockhaus_, Mar 17 2004
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