A323392 Positive integers that have a record number of divisors in Eisenstein integers.

1, 2, 3, 6, 12, 18, 21, 36, 42, 84, 126, 168, 252, 420, 504, 546, 1008, 1092, 1638, 2184, 3276, 5460, 6552, 7644, 9828, 10374, 13104, 15288, 16380, 20748, 31122, 38220, 41496, 62244, 103740, 124488, 145236, 186732, 207480, 248976, 290472, 311220, 435708, 622440, 726180, 871416

Offset: 1

Author

Jianing Song, Jan 13 2019

Keywords

• nonn

Comments

Indices of records in A319442.

Analog of A002182 and A279254, which list the positive integers that have a record number of divisors in rational integers and Gaussian integers respectively.

It seems that 21 is the largest odd term.

Examples

			252 has 60 divisors up to association in Eisenstein integers, more than any previous positive integers, so 252 is a term.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..100
• Wikipedia, Eisenstein integer

Crossrefs

Cf. A002182, A279254, A319442.

For the number of divisors of a(n) see A323393.

Programs

Maple

vmax:= 0: recinds:= NULL:
for n from 1 to 100000 do
    v := A319442(n);
    if v > vmax then vmax:= v; recinds:= recinds, n fi
od:
recinds; # Peter Luschny, Jan 19 2019

Mathematica

f[p_, e_] := Switch[Mod[p, 3], 0, 2*e + 1, 1, (e + 1)^2, 2, e + 1]; eisNumDiv[1] = 1; eisNumDiv[n_] := Times @@ f @@@ FactorInteger[n]; seq = {}; emax = 0; Do[eis = eisNumDiv[n]; If[eis > emax, emax = eis; AppendTo[seq, n]], {n, 1, 10^6}]; seq (* Amiram Eldar, Mar 02 2020 *)

PARI

my(r=0, t); for(n=1, 10^6, t=A319442(n); if(t>r, r=t; print1(n, ", ")));