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A323393
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a(n) is the number of divisors of A323392(n) in Eisenstein integers.
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2
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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FORMULA
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EXAMPLE
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252 has 60 divisors up to association in Eisenstein integers, more than any previous positive integers, so 60 is a term.
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MATHEMATICA
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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 *)
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PROG
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(PARI)
my(r=0, t); for(n=1, 10^6, t=A319442(n); if(t>r, r=t; print1(r, ", ")));
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CROSSREFS
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For the numbers whose number of divisors set new records see A323392.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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