%I #29 Oct 09 2023 12:52:17
%S 245784,288288,320320,480480,911064,1755600,1796760,2066400,2511600,
%T 2841696,3447549,3511200,3686760,4914000,5116320,6144600,7022400,
%U 7195320,7255872,7534800,8796480
%N Lenstra numbers with 6 divisors in a single residue class.
%C Numbers N such that there exists a residue r and a modulus s with s^3 > N > s > r > 0 and gcd(r,s)=1 such that N has at least 6 divisors in the residue class r modulo s.
%C It can be shown that this sequence is infinite.
%C No case is known with more than 6 such divisors.
%C The first 10 terms were found by Hendrik Lenstra.
%C Additional terms up to a(20) were supplied by _David Broadhurst_.
%H Henri Cohen, <a href="https://eudml.org/doc/182154">Diviseurs appartenant à une même classe résiduelle</a>, Séminaire de Théorie des Nombres de Bordeaux (1982-1983), Volume 12, pp. 1-12.
%H D. Coppersmith, N. Howgrave-Graham and S. V. Nagaraj, <a href="https://doi.org/10.1090/S0025-5718-07-02007-8">Divisors in residue classes, constructively</a>, Math. Comp., 77 (2008), 531-545.
%H H. W. Lenstra, <a href="https://doi.org/10.1090/S0025-5718-1984-0726007-1">Divisors in residue classes</a>, Math. Comp., 42 (1984), 331-340. See Table 2.
%H Paul Zimmermann, <a href="/A146544/a146544.c.txt">divisorslenstra.c</a>.
%e a(7) = 1796760 has 6 divisors congruent to 3 modulo 137, namely 3, 140, 414, 3565, 7812, 19320, and 6 divisors congruent to 93 modulo 137, namely 93, 230, 504, 4340, 12834, 598920.
%e a(17) = 7022400 has 6 divisors for 4 classes r mod s=199, namely r=4, 8, 11 and 22. - _Paul Zimmermann_, Jan 18 2018
%o (C) See the Paul Zimmermann link.
%K hard,nice,nonn
%O 1,1
%A _David Broadhurst_, Oct 31 2008
%E Previous values checked by and a(21) from _Paul Zimmermann_, Jan 18 2018