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A181451
Numbers n such that 13 is the largest prime factor of n^2 - 1.
2
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
1,1
COMMENTS
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.
MATHEMATICA
Select[Range[250000], FactorInteger[#^2-1][[-1, 1]]==13&]
PROG
(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
(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
KEYWORD
fini,nonn,full
AUTHOR
Artur Jasinski, Oct 21 2010
STATUS
approved