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

1,2

Comments

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

Links

Table of n, a(n) for n=1..21.

Example

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.

Sequence in context: A030574 A325652 A283653 * A162657 A333046 A305794

Adjacent sequences: A375635 A375636 A375637 * A375639 A375640 A375641

Keyword

nonn,more

Author

Amiram Eldar, Aug 22 2024

Status

approved