A384370 Squarefree integers m such that there are precisely 5 groups of order m.

273, 399, 651, 741, 777, 1209, 1281, 1365, 1407, 1443, 1533, 1659, 1677, 1767, 1995, 2037, 2109, 2163, 2289, 2379, 2451, 2613, 2847, 2919, 3003, 3171, 3297, 3423, 3441, 3477, 3705, 3783, 3801, 3819, 3885, 3999, 4017, 4053, 4161, 4179, 4251, 4389, 4503, 4641, 4683, 4773, 4809, 4953

Offset: 1

Author

Robin Jones, May 27 2025

Keywords

• nonn

Comments

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.

This is a subsequence of A054397.

This sequence is infinite.

Examples

			273 is in this sequence as 273 is squarefree, and A000001(273) = 5.
		

Links

• Robin Jones, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054397.

Programs

Mathematica

Select[Range[5000], SquareFreeQ[#]&&FiniteGroupCount[#] == 5 &] (* James C. McMahon, May 31 2025 *)