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

%I A181462 #21 Dec 20 2024 17:40:54
%S A181462 58,117,119,176,235,237,296,353,471,530,532,589,591,650,766,827,945,
%T A181462 1002,1061,1063,1179,1297,1299,1535,1592,1594,1651,1769,1828,1887,
%U A181462 1889,2066,2184,2241,2243,2300,2302,2479,2536,2774,2951,3126,3244,3305,3421
%N A181462 Numbers k such that 59 is the largest prime factor of k^2-1.
%C A181462 Numbers k such that A076605(k) = 59.
%C A181462 Sequence is finite, for proof see A175607.
%C A181462 Search for terms can be restricted to the range from 2 to A175607(17) = 41257182408961; primepi(59) = 17.
%H A181462 Artur Jasinski, <a href="/A181462/b181462.txt">Table of n, a(n) for n = 1..634</a>
%t A181462 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_ *)
%t A181462 Select[Range[10000],Max[Transpose[FactorInteger[#^2-1]][[1]]]==59&] (* _Harvey P. Dale_, Nov 13 2010 *)
%o A181462 (PARI) for(k=2,1e9,vecmax(factor(k^2-1)[,1])==59 & print1(k",")) \\ _M. F. Hasler_, Nov 13 2010
%o A181462 (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
%o A181462 (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
%Y A181462 Cf. A076605, A175607, A181447-A181461, A181463-A181470, A181568.
%K A181462 fini,full,nonn
%O A181462 1,1
%A A181462 _Artur Jasinski_, Oct 21 2010