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

 

Logo
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, Seminaire 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 of Divisors in residue classes by H. W. Lenstra.

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 28 18:53 EDT 2022. Contains 357081 sequences. (Running on oeis4.)