%I #48 Aug 21 2022 09:14:51
%S 0,1,7,49,91,637,1729,8281,12103,53599,157339,375193,1983163,4877509,
%T 13882141,85276009,180467833,596932063,3428888827,4178524441,
%U 7760116819,29249671087,36412855843,147442219561,254889990901,473367125959,1784229936307,2439661341481
%N Squared radii of circles around a point of the hexagonal lattice that contain a record number of lattice points.
%C It appears that this is also the sequence of numbers with a record number of divisors all of whose prime factors are of the form 3k + 1. - _Amiram Eldar_, Sep 12 2019 [This is correct, see A343771. - _Jianing Song_, May 19 2021]
%C Indices of records of A004016. Apart from the first term, also indices of records of A002324. - _Jianing Song_, May 20 2021
%H Jianing Song, <a href="/A230655/b230655.txt">Table of n, a(n) for n = 1..247</a> (all terms <= 10^75.)
%e a(2)=7 because a circle with radius sqrt(7) around the lattice point at (0,0) is the first circle that passes through more lattice points than a circle with radius 1, which passes through 6 points. The 12 hit points are (+-1/2,+-3*sqrt(3)/2), (+-2,+-sqrt(3)), (+-5/2, +-sqrt(3)/2).
%o (PARI) my(v=list_A344473(10^15), rec=0); print1(0, ", "); for(n=1, #v, if(numdiv(v[n])>rec, rec=numdiv(v[n]); print1(v[n], ", "))) \\ _Jianing Song_, May 20 2021, see program for A344473
%Y Cf. A004016, A002324.
%Y Cf. A003136 (all occurring squared radii), A198799 (common terms), A230656 (index positions of records), A344472 (records).
%Y Apart from the first term, subsequence of A343771.
%Y Indices of records of Sum_{d|n} kronecker(m, d): this sequence (m=-3), A071383 (m=-4, similar sequence for square lattice), A279541 (m=-6).
%K nonn
%O 1,3
%A _Hugo Pfoertner_, Oct 27 2013
%E Offset corrected by _Jianing Song_, May 20 2021