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A323393
a(n) is the number of divisors of A323392(n) in Eisenstein integers.
2
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
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
For the numbers whose number of divisors set new records see A323392.
Sequence in context: A120752 A236759 A134695 * A190674 A188399 A047284
KEYWORD
nonn
AUTHOR
Jianing Song, Jan 13 2019
STATUS
approved