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%I #9 Jun 25 2022 21:57:10
%S 0,0,1,2,2,2,2,6,4,2,22,28,42,72,112,288,420,720,1568,1920,3512,16560,
%T 19686,16028,71280,182160,184320,552960,2925648,4885160,12080640,
%U 32861900,71559680,77631750,217165824,604653336,368858880,4069377144,7919402400,17537715360,87352688640,127718553600
%N Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of z-x.
%C a(n) <= A061033(n).
%C n=61 gives the smallest example where the value of x is not maximal (cf. A061030) and the value of z is not minimal.
%C Apparently we have x < y < z for all n > 9. If so, using strict inequalities x < y < z in the definition would make the sequence undefined for n < 3 and affect only a(9) by switching from 9! = 70*72*72 to 9! = 63*72*80.
%H Max Alekseyev, <a href="/A355192/b355192.txt">Table of n, a(n) for n = 0..100</a>
%Y Cf. A061030, A061031, A061032, A061033, A060776, A060777, A060795, A060796, A200743, A200744, A355189, A355190, A355191.
%K nonn
%O 0,4
%A _Max Alekseyev_, Jun 23 2022
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