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%I #7 Aug 22 2024 09:17:49
%S 1,2,3,4,5,17,42,43,138,125,220,33,387,1766,3269,7014,1398,1399,1958,
%T 19143,30759
%N 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.
%C a(n) is the least k > 0 such that A375636(k) = n.
%e The n values m(i) such that m(i)! is an infinitary divisor of a(n)! for n = 1..12 are:
%e n | a(n) | m(i), i = 1..n
%e ---+------+-----------------------------------------
%e 1 | 1 | 1
%e 2 | 2 | 1, 2
%e 3 | 3 | 1, 2, 3
%e 4 | 4 | 1, 2, 3, 4
%e 5 | 5 | 1, 2, 3, 4, 5
%e 6 | 17 | 1, 2, 6, 15, 16, 17
%e 7 | 42 | 1, 2, 3, 4, 5, 6, 42
%e 8 | 43 | 1, 2, 3, 4, 5, 6, 42, 43
%e 9 | 138 | 1, 2, 3, 4, 5, 6, 7, 8, 138
%e 10 | 125 | 1, 2, 3, 4, 5, 6, 7, 8, 124, 125
%e 11 | 220 | 1, 2, 3, 4, 5, 6, 7, 8, 218, 219, 220
%e 12 | 33 | 1, 2, 3, 4, 5, 6, 28, 29, 30, 31, 32, 33
%Y Cf. A000142, A037445, A077609, A375635, A375636.
%K nonn,more
%O 1,2
%A _Amiram Eldar_, Aug 22 2024