%I #11 Jun 30 2022 05:57:12
%S 1,5,25,35,175,385,1225,1925,5005,13475,25025,85085,175175,425425,
%T 1616615,2977975,8083075,32757725,37182145,56581525,185910725,
%U 622396775,929553625,1301375075,4647768125,5391411025,14315125825,26957055125,37739877175,134785275625
%N Highly composite 5-rough numbers: numbers that are divisible by neither 2 nor 3 whose number of divisors reaches a record.
%H Amiram Eldar, <a href="/A343734/b343734.txt">Table of n, a(n) for n = 1..208</a>
%e number of
%e divisors
%e n a(n) prime factorization of a(n) of a(n)
%e -- ----- ---------------------------- ---------
%e 1 1 - 1
%e 2 5 5 2
%e 3 25 5^2 3
%e 4 35 5 * 7 4
%e 5 175 5^2 * 7 6
%e 6 385 5 * 7 * 11 8
%e 7 1225 5^2 * 7^2 9
%e 8 1925 5^2 * 7 * 11 12
%e 9 5005 5 * 7 * 11 * 13 16
%e 10 13475 5^2 * 7^2 * 11 18
%e 11 25025 5^2 * 7 * 11 * 13 24
%e 12 85085 5 * 7 * 11 * 13 * 17 32
%Y Cf. A000005, A002182, A007310, A053624.
%K nonn
%O 1,2
%A _Jon E. Schoenfield_, Jun 14 2021