The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A146544 Lenstra numbers with 6 divisors in a single residue class. 1
 245784, 288288, 320320, 480480, 911064, 1755600, 1796760, 2066400, 2511600, 2841696, 3447549, 3511200, 3686760, 4914000, 5116320, 6144600, 7022400, 7195320, 7255872, 7534800, 8796480 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS 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. It can be shown that this sequence is infinite. No case is known with more than 6 such divisors. The first 10 terms were found by Hendrik Lenstra. Additional terms up to a(20) were supplied by David Broadhurst. LINKS Table of n, a(n) for n=1..21. Henri Cohen, Diviseurs appartenant à une même classe résiduelle, Séminaire de Théorie des Nombres de Bordeaux (1982-1983), Volume 12, pp. 1-12. D. Coppersmith, N. Howgrave-Graham and S. V. Nagaraj, Divisors in residue classes, constructively, Math. Comp., 77 (2008), 531-545. H. W. Lenstra, Divisors in residue classes, Math. Comp., 42 (1984), 331-340. See Table 2. Paul Zimmermann, divisorslenstra.c. EXAMPLE 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. 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 PROG (C) See the Paul Zimmermann link. CROSSREFS Sequence in context: A187771 A233632 A251856 * A237313 A321039 A230525 Adjacent sequences: A146541 A146542 A146543 * A146545 A146546 A146547 KEYWORD hard,nice,nonn AUTHOR David Broadhurst, Oct 31 2008 EXTENSIONS Previous values checked by and a(21) from Paul Zimmermann, Jan 18 2018 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified August 6 14:16 EDT 2024. Contains 374974 sequences. (Running on oeis4.)