A355192 Factorial splitting: write n! = x*y*z with x <= y <= z and minimal z-x; sequence gives value of z-x.

0, 0, 1, 2, 2, 2, 2, 6, 4, 2, 22, 28, 42, 72, 112, 288, 420, 720, 1568, 1920, 3512, 16560, 19686, 16028, 71280, 182160, 184320, 552960, 2925648, 4885160, 12080640, 32861900, 71559680, 77631750, 217165824, 604653336, 368858880, 4069377144, 7919402400, 17537715360, 87352688640, 127718553600

Offset: 0

Author

Max Alekseyev, Jun 23 2022

Keywords

• nonn

Comments

a(n) <= A061033(n).

n=61 gives the smallest example where the value of x is not maximal (cf. A061030) and the value of z is not minimal.

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.

Links

• Max Alekseyev, Table of n, a(n) for n = 0..100

Crossrefs

Cf. A061030, A061031, A061032, A061033, A060776, A060777, A060795, A060796, A200743, A200744, A355189, A355190, A355191.