

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.


LINKS



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



KEYWORD

hard,nice,nonn


AUTHOR



EXTENSIONS



STATUS

approved



