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.

a(2)-a(25)=total number of terms in A181447-A181470.

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.

Wikipedia, Størmer's theorem

Crossrefs

Cf. A175607, A175901-A175904, A181447-A181470.

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