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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
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
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
For the number of divisors of a(n) see A323393.
Sequence in context: A286906 A125867 A032727 * A174801 A324177 A280681
KEYWORD
nonn
AUTHOR
Jianing Song, Jan 13 2019
STATUS
approved