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

1,2

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.

Links

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

Wikipedia, Eisenstein integer

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A002183, A302249, A319442.

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

Sequence in context: A120752 A236759 A134695 * A190674 A188399 A047284

Adjacent sequences: A323390 A323391 A323392 * A323394 A323395 A323396

Keyword

nonn

Author

Jianing Song, Jan 13 2019

Status

approved