

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
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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 (19821983), Volume 12, pp. 112.
D. Coppersmith, N. HowgraveGraham and S. V. Nagaraj, Divisors in residue classes, constructively, Math. Comp., 77 (2008), 531545.
H. W. Lenstra, Divisors in residue classes, Math. Comp., 42 (1984), 331340.
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



