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%I #15 Sep 08 2022 08:45:54
%S 60,62,121,123,184,243,245,365,367,426,428,487,489,550,609,611,794,
%T 1036,1099,1160,1219,1221,1343,1463,1585,1646,1709,1768,1770,1951,
%U 2014,2073,2256,2319,2439,2441,2500,2561,2624,2807,2927,3173,3537,3539,3659,3781
%N Numbers n such that 61 is the largest prime factor of n^2-1.
%C Sequence is finite, for proof see A175607.
%C Search for terms can be restricted to the range from 2 to A175607(18) = 63774701665793; primepi(61) = 18.
%H A. Jasinski, <a href="/A181463/b181463.txt">Table of n, a(n) for n = 1..799</a>
%t 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_ *)
%t Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==61&]
%o (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
%o (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
%Y Cf. A175607, A181447-A181462, A181464-A181470, A181568.
%K fini,nonn
%O 1,1
%A _Artur Jasinski_, Oct 21 2010
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