%I #18 Mar 02 2020 09:39:00

%S 1,2,3,6,12,18,21,36,42,84,126,168,252,420,504,546,1008,1092,1638,

%T 2184,3276,5460,6552,7644,9828,10374,13104,15288,16380,20748,31122,

%U 38220,41496,62244,103740,124488,145236,186732,207480,248976,290472,311220,435708,622440,726180,871416

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

%C Indices of records in A319442.

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

%C It seems that 21 is the largest odd term.

%H Amiram Eldar, <a href="/A323392/b323392.txt">Table of n, a(n) for n = 1..100</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Eisenstein_integer">Eisenstein integer</a>

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

%p vmax:= 0: recinds:= NULL:

%p for n from 1 to 100000 do

%p v := A319442(n);

%p if v > vmax then vmax:= v; recinds:= recinds, n fi

%p od:

%p recinds; # _Peter Luschny_, Jan 19 2019

%t 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 *)

%o (PARI)

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

%Y Cf. A002182, A279254, A319442.

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

%K nonn

%O 1,2

%A _Jianing Song_, Jan 13 2019