A181462 Numbers k such that 59 is the largest prime factor of k^2-1.

58, 117, 119, 176, 235, 237, 296, 353, 471, 530, 532, 589, 591, 650, 766, 827, 945, 1002, 1061, 1063, 1179, 1297, 1299, 1535, 1592, 1594, 1651, 1769, 1828, 1887, 1889, 2066, 2184, 2241, 2243, 2300, 2302, 2479, 2536, 2774, 2951, 3126, 3244, 3305, 3421

Offset: 1

Author

Artur Jasinski, Oct 21 2010

Keywords

• fini
• full
• nonn

Comments

Numbers k such that A076605(k) = 59.

Sequence is finite, for proof see A175607.

Search for terms can be restricted to the range from 2 to A175607(17) = 41257182408961; primepi(59) = 17.

Links

• Artur Jasinski, Table of n, a(n) for n = 1..634

Crossrefs

Cf. A076605, A175607, A181447-A181461, A181463-A181470, A181568.

Programs

Magma

[ n: n in [2..300000] | m eq 59 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011

Magma

p:=(97*89*83*79*73*71)^5 *(67*61*59*53*47*43*41)^6 *(37*31*29)^7 *(23*19*17)^8 *13^9 *11^10 *7^13 *5^15 *3^23 *2^36; [ n: n in [2..50000000] | p mod (n^2-1) eq 0 and (D[#D] eq 59 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 20 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 < 3222617400, If[GCD[jj, n^2 - 1] == n^2 - 1, k = FactorInteger[n^2 - 1]; kk = Last[k][[1]]; If[kk == 59, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[10000],Max[Transpose[FactorInteger[#^2-1]][[1]]]==59&] (* Harvey P. Dale, Nov 13 2010 *)

PARI

for(k=2,1e9,vecmax(factor(k^2-1)[,1])==59 & print1(k",")) \\ M. F. Hasler, Nov 13 2010