A181463 Numbers k such that 61 is the largest prime factor of k^2-1.

60, 62, 121, 123, 184, 243, 245, 365, 367, 426, 428, 487, 489, 550, 609, 611, 794, 1036, 1099, 1160, 1219, 1221, 1343, 1463, 1585, 1646, 1709, 1768, 1770, 1951, 2014, 2073, 2256, 2319, 2439, 2441, 2500, 2561, 2624, 2807, 2927, 3173, 3537, 3539, 3659, 3781

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• fini
• full
• nonn

Comments

Numbers k such that A076605(k) = 61.

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(18) = 63774701665793; primepi(61) = 18.

Links

• Artur Jasinski, Table of n, a(n) for n = 1..799

Crossrefs

Cf. A076605, A175607, A181447-A181462, A181464-A181470, A181568.

Programs

Magma

[ n: n in [2..300000] | m eq 61 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011

Mathematica

jj = 2^36*3^23*5^15*7^13*11^10*13^9*17^8*19^8*23^8*29^7*31^7*37^7*41^6 *43^6*47^6*53^6*59^6*61^6*67^6*71^5*73^5*79^5*83^5*89^5*97^5; rr = {}; n = 2; While[n < 14000000, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 61, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==61&]

PARI

is(n)=n=n^2-1; forprime(p=2, 59, n/=p^valuation(n, p)); n>1 && 61^valuation(n, 61)==n \\ Charles R Greathouse IV, Jul 01 2013