A181451 Numbers k such that 13 is the largest prime factor of k^2 - 1.

12, 14, 25, 27, 51, 53, 64, 79, 129, 131, 155, 181, 209, 274, 287, 337, 391, 649, 701, 703, 727, 846, 1249, 1351, 1457, 1574, 2001, 3431, 4159, 8191, 8449, 13311, 21295, 246401

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• fini
• nonn
• full

Comments

Numbers k such that A076605(k) = 13.

Sequence is finite and complete, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(6) = 246401; primepi(13) = 6.

Crossrefs

Row 6 of A223701.

Cf. A076605, A175607, A181447-A181450, A181452-A181470, A181568.

Programs

Magma

[ n: n in [2..250000] | m eq 13 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011

Mathematica

Select[Range[250000], FactorInteger[#^2-1][[-1, 1]]==13&]

PARI

is(n)=n=n^2-1; forprime(p=2, 11, n/=p^valuation(n, p)); n>1 && 13^valuation(n, 13)==n \\ Charles R Greathouse IV, Jul 01 2013