cp's OEIS Frontend

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

%I A323392 #18 Mar 02 2020 09:39:00
%S A323392 1,2,3,6,12,18,21,36,42,84,126,168,252,420,504,546,1008,1092,1638,
%T A323392 2184,3276,5460,6552,7644,9828,10374,13104,15288,16380,20748,31122,
%U A323392 38220,41496,62244,103740,124488,145236,186732,207480,248976,290472,311220,435708,622440,726180,871416
%N A323392 Positive integers that have a record number of divisors in Eisenstein integers.
%C A323392 Indices of records in A319442.
%C A323392 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 A323392 It seems that 21 is the largest odd term.
%H A323392 Amiram Eldar, <a href="/A323392/b323392.txt">Table of n, a(n) for n = 1..100</a>
%H A323392 Wikipedia, <a href="https://en.wikipedia.org/wiki/Eisenstein_integer">Eisenstein integer</a>
%e A323392 252 has 60 divisors up to association in Eisenstein integers, more than any previous positive integers, so 252 is a term.
%p A323392 vmax:= 0: recinds:= NULL:
%p A323392 for n from 1 to 100000 do
%p A323392     v := A319442(n);
%p A323392     if v > vmax then vmax:= v; recinds:= recinds, n fi
%p A323392 od:
%p A323392 recinds; # _Peter Luschny_, Jan 19 2019
%t A323392 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 A323392 (PARI)
%o A323392 my(r=0, t); for(n=1, 10^6, t=A319442(n); if(t>r, r=t; print1(n, ", ")));
%Y A323392 Cf. A002182, A279254, A319442.
%Y A323392 For the number of divisors of a(n) see A323393.
%K A323392 nonn
%O A323392 1,2
%A A323392 _Jianing Song_, Jan 13 2019