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a(n) is the smallest number with exactly n divisors that are greater than or equal to 5.
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%I #9 Aug 18 2024 12:22:37

%S 5,10,18,24,30,48,80,60,90,192,144,120,210,180,450,240,560,1600,5120,

%T 360,630,3465,900,960,2240,720,2800,840,1890,10010,5184,1260,3150,

%U 17325,36864,1680,5670,2880,11200,15360,3600,19600,99225,2520,6930,6480,70000,61440

%N a(n) is the smallest number with exactly n divisors that are greater than or equal to 5.

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%t DeleteDuplicates[SortBy[Table[{n,Count[Divisors[n],_?(#>4&)]},{n,100000}],Last],GreaterEqual[ #1[[2]],#2[[2]]]&][[;;,1]] (* _Harvey P. Dale_, Aug 18 2024 *)

%o (PARI) a(n) = my(k=1); while (sumdiv(k, d, (d>=5)) != n, k++); k; \\ _Michel Marcus_, Jan 20 2023

%Y Cf. A005179, A338648, A359955, A359957.

%K nonn

%O 1,1

%A _Ilya Gutkovskiy_, Jan 19 2023