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A323393 a(n) is the number of divisors of A323392(n) in Eisenstein integers.

%I A323393 #17 Mar 02 2020 09:39:06
%S A323393 1,2,3,6,9,10,12,15,24,36,40,48,60,72,80,96,100,144,160,192,240,288,
%T A323393 320,324,336,384,400,432,480,576,640,648,768,960,1152,1280,1296,1344,
%U A323393 1536,1600,1728,1920,2160,2560,2592,2880,3200,3456,3600,3840,4320,4608,5120,5760,6144,6400,7200,7680
%N A323393 a(n) is the number of divisors of A323392(n) in Eisenstein integers.
%C A323393 Records in A319442.
%C A323393 Analog of A002183 and A302249, which list the records of number of divisors in rational integers and Gaussian integers respectively.
%C A323393 It seems that 15 is the largest odd term.
%H A323393 Amiram Eldar, <a href="/A323393/b323393.txt">Table of n, a(n) for n = 1..100</a>
%H A323393 Wikipedia, <a href="https://en.wikipedia.org/wiki/Eisenstein_integer">Eisenstein integer</a>
%F A323393 a(n) = A319442(A323392(n)).
%e A323393 252 has 60 divisors up to association in Eisenstein integers, more than any previous positive integers, so 60 is a term.
%t A323393 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, eis]], {n, 1, 10^6}]; seq (* _Amiram Eldar_, Mar 02 2020 *)
%o A323393 (PARI)
%o A323393 my(r=0, t); for(n=1, 10^6, t=A319442(n); if(t>r, r=t; print1(r, ", ")));
%Y A323393 Cf. A002183, A302249, A319442.
%Y A323393 For the numbers whose number of divisors set new records see A323392.
%K A323393 nonn
%O A323393 1,2
%A A323393 _Jianing Song_, Jan 13 2019