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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
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.
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
KEYWORD
nonn,more
AUTHOR
Amiram Eldar, Aug 22 2024
STATUS
approved