A181460 Numbers k such that 47 is the largest prime factor of k^2-1.

46, 48, 93, 95, 142, 187, 189, 281, 375, 377, 424, 469, 610, 657, 659, 704, 751, 753, 892, 988, 1033, 1035, 1082, 1174, 1223, 1270, 1364, 1409, 1597, 1599, 1691, 1693, 1926, 1973, 1975, 2022, 2069, 2161, 2255, 2351, 2443, 2584, 2727, 2913, 2915, 3009

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• fini
• full
• nonn

Comments

Numbers k such that A076605(k) = 47.

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(15) = 2218993446251; primepi(47) = 15.

Links

• Artur Jasinski, Table of n, a(n) for n = 1..433

Crossrefs

Cf. A076605, A175607, A181447-A181459, A181461-A181470, A181568.

Programs

Magma

[ n: n in [2..300000] | m eq 47 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011

Mathematica

Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==47&]

PARI

is(n)=n=n^2-1; forprime(p=2, 43, n/=p^valuation(n, p)); n>1 && 47^valuation(n, 47)==n \\ Charles R Greathouse IV, Jul 01 2013