A375638 a(n) is the least positive integer k such that k! has exactly n infinitary divisors that are factorials, or -1 if no such number exists.

1, 2, 3, 4, 5, 17, 42, 43, 138, 125, 220, 33, 387, 1766, 3269, 7014, 1398, 1399, 1958, 19143, 30759

Offset: 1

Author

Amiram Eldar, Aug 22 2024

Keywords

• nonn
• more

Comments

a(n) is the least k > 0 such that A375636(k) = n.

Examples

			The n values m(i) such that m(i)! is an infinitary divisor of a(n)! for n = 1..12 are:
   n | a(n) | m(i), i = 1..n
  ---+------+-----------------------------------------
   1 |   1  | 1
   2 |   2  | 1, 2
   3 |   3  | 1, 2, 3
   4 |   4  | 1, 2, 3, 4
   5 |   5  | 1, 2, 3, 4, 5
   6 |  17  | 1, 2, 6, 15, 16, 17
   7 |  42  | 1, 2, 3, 4, 5, 6, 42
   8 |  43  | 1, 2, 3, 4, 5, 6, 42, 43
   9 | 138  | 1, 2, 3, 4, 5, 6, 7, 8, 138
  10 | 125  | 1, 2, 3, 4, 5, 6, 7, 8, 124, 125
  11 | 220  | 1, 2, 3, 4, 5, 6, 7, 8, 218, 219, 220
  12 |  33  | 1, 2, 3, 4, 5, 6, 28, 29, 30, 31, 32, 33
		

Crossrefs

Cf. A000142, A037445, A077609, A375635, A375636.