This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384370 #15 May 31 2025 19:20:44 %S A384370 273,399,651,741,777,1209,1281,1365,1407,1443,1533,1659,1677,1767, %T A384370 1995,2037,2109,2163,2289,2379,2451,2613,2847,2919,3003,3171,3297, %U A384370 3423,3441,3477,3705,3783,3801,3819,3885,3999,4017,4053,4161,4179,4251,4389,4503,4641,4683,4773,4809,4953 %N A384370 Squarefree integers m such that there are precisely 5 groups of order m. %C A384370 These are precisely the squarefree integers m such that 3|m, there are exactly two prime factors of m which are congruent to 1 modulo 3, and there are no other relations of the form p = 1 mod q for any pair of prime factors p, q of m. %C A384370 This is a subsequence of A054397. %C A384370 This sequence is infinite. %H A384370 Robin Jones, <a href="/A384370/b384370.txt">Table of n, a(n) for n = 1..10000</a> %e A384370 273 is in this sequence as 273 is squarefree, and A000001(273) = 5. %t A384370 Select[Range[5000], SquareFreeQ[#]&&FiniteGroupCount[#] == 5 &] (* _James C. McMahon_, May 31 2025 *) %Y A384370 Cf. A054397. %K A384370 nonn %O A384370 1,1 %A A384370 _Robin Jones_, May 27 2025