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

1, 2, 3, 6, 9, 10, 12, 15, 24, 36, 40, 48, 60, 72, 80, 96, 100, 144, 160, 192, 240, 288, 320, 324, 336, 384, 400, 432, 480, 576, 640, 648, 768, 960, 1152, 1280, 1296, 1344, 1536, 1600, 1728, 1920, 2160, 2560, 2592, 2880, 3200, 3456, 3600, 3840, 4320, 4608, 5120, 5760, 6144, 6400, 7200, 7680

Offset: 1

Author

Jianing Song, Jan 13 2019

Keywords

• nonn

Comments

Records in A319442.

Analog of A002183 and A302249, which list the records of number of divisors in rational integers and Gaussian integers respectively.

It seems that 15 is the largest odd term.

Examples

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

Links

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

Crossrefs

Cf. A002183, A302249, A319442.

For the numbers whose number of divisors set new records see A323392.

Programs

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, eis]], {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(r, ", ")));

Formula

a(n) = A319442(A323392(n)).