A372294 The smallest number k which, when written in base n, has a factorization k = f_1*f_2*...*f_r where f_i >= 1 and the digits of {k, f_1, f_2, ..., f_r} together contain the digits 0,1,...,(n-1) exactly once. Set a(n) = -1 if no such k exists.

-1, -1, -1, -1, -1, 104, 440, 1440, 4830, 15552, 72240, 282240, 1039104, 4244940, 24108000

Offset: 2

Author

Chai Wah Wu, Apr 25 2024

Keywords

• sign
• base
• more

Comments

Similar to A372249, except that here the factors are allowed to be equal to 1. Differs from A372249 at n = 7, 10, 12, 15, ...

Examples

			a(7)  =      104 = 1*4*26
a(8)  =      440 = 2*4*5*11
a(9)  =     1440 = 3*4*5*24
a(10) =     4830 = 1*2*5*7*69
a(11) =    15552 = 2*3*6*8*54
a(12) =    72240 = 1*4*6*7*430
a(13) =   282240 = 2*3*5*7*21*64
a(14) =  1039104 = 2*3*4*6*8*11*82
a(15) =  4244940 = 1*2*3*7*9*10*1123
a(16) = 24108000 = 3*4*5*7*10*41*140
		

Crossrefs

Cf. A372249, A372053, A370970, A371958.

Formula

a(n) <= A372249(n).