A340516 Let p_i (i=1..m) denote the primes <= n, and let e_i be the maximum number such that p_i^e_i <= n; then a(n) = Product_{i=1..m} p_i^(2*e_i-1).

1, 2, 6, 24, 120, 120, 840, 3360, 30240, 30240, 332640, 332640, 4324320, 4324320, 4324320, 17297280, 294053760, 294053760, 5587021440, 5587021440, 5587021440, 5587021440, 128501493120, 128501493120, 3212537328000, 3212537328000, 28912835952000, 28912835952000, 838472242608000

Offset: 1

Author

N. J. A. Sloane, Feb 03 2021

Keywords

• nonn

Comments

This is a lower bound on A340515.

References

• Heffernan, Robert, Des MacHale, and Brendan McCann. "Cayley’s Theorem Revisited: Embeddings of Small Finite Groups." Mathematics Magazine 91.2 (2018): 103-111.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..2242
• Heffernan, Robert, Des MacHale, and Brendan McCann, Minimal embeddings of small finite groups, arXiv:1706.09286 [math.GR], 2017. See Lemma 2.

Crossrefs

Cf. A340514, A340515.

Programs

Mathematica

{1}~Join~Table[Times @@ Map[#^(2 Floor@ Log[#, n] - 1) &, Prime@ Range@ PrimePi@ n], {n, 2, 30}] (* Michael De Vlieger, Feb 23 2022 *)