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

1,2

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.

Links

Amiram Eldar, Table of n, a(n) for n = 1..100

Wikipedia, Eisenstein integer

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002182, A279254, A319442.

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

Sequence in context: A286906 A125867 A032727 * A174801 A324177 A280681

Adjacent sequences: A323389 A323390 A323391 * A323393 A323394 A323395

Keyword

nonn

Author

Jianing Song, Jan 13 2019

Status

approved