A181471 a(n) = number of numbers of the form k^2-1 having n-th prime as largest prime divisor.

1, 4, 8, 16, 20, 34, 47, 72, 95, 126, 168, 208, 262, 343, 433, 507, 634, 799, 976, 1146, 1439, 1698, 2082, 2371, 2734

Offset

1,2

Comments

Theorem: zero does not occur in this sequence. Proof: (p-1)^2-1=(p-2)p. This means that p is greatest prime divisor of (p-1)^2-1 for every p.

An effective abc conjecture (c < rad(abc)^2) would imply that a(24)-a(33) are (2371, 2734, 3360, 4022, 4637, 5575, 6424, 7268, 8351, 9661). - Lucas A. Brown, Oct 01 2022

Links

Table of n, a(n) for n=1..25.

Florian Luca and Filip Najman, On the largest prime factor of x^2-1, arXiv:1005.1533 [math.NT], 2010.

Florian Luca and Filip Najman, On the largest prime factor of x^2-1, Mathematics of Computation 80 (2011), 429-435. (Paper has errata that was posted on the MOC website.)

Wikipedia, Størmer's theorem.

Crossrefs

Row lengths of A223701.

Cf. A039915, A175607.

Sequence in context: A312805 A312806 A036693 * A272753 A272804 A237990

Adjacent sequences: A181468 A181469 A181470 * A181472 A181473 A181474

Keyword

nonn,hard,more

Author

Artur Jasinski, Oct 21-22 2010

Extensions

Wrong terms a(24)-a(25) removed by Lucas A. Brown, Oct 01 2022

a(24)-a(25) from David A. Corneth, Oct 01 2022

Status

approved