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A323392 Positive integers that have a record number of divisors in Eisenstein integers. 2
1, 2, 3, 6, 12, 18, 21, 36, 42, 84, 126, 168, 252, 420, 504, 546, 1008, 1092, 1638, 2184, 3276, 5460, 6552, 7644, 9828, 10374, 13104, 15288, 16380, 20748, 31122, 38220, 41496, 62244, 103740, 124488, 145236, 186732, 207480, 248976, 290472, 311220, 435708, 622440, 726180, 871416 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Indices of records in A319442.

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

It seems that 21 is the largest odd term.

LINKS

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

Wikipedia, Eisenstein integer

EXAMPLE

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

MAPLE

vmax:= 0: recinds:= NULL:

for n from 1 to 100000 do

    v := A319442(n);

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

od:

recinds; # Peter Luschny, Jan 19 2019

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, n]], {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(n, ", ")));

CROSSREFS

Cf. A002182, A279254, A319442.

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

Sequence in context: A286906 A125867 A032727 * A174801 A324177 A280681

Adjacent sequences:  A323389 A323390 A323391 * A323393 A323394 A323395

KEYWORD

nonn

AUTHOR

Jianing Song, Jan 13 2019

STATUS

approved

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Last modified January 20 18:38 EST 2022. Contains 350472 sequences. (Running on oeis4.)