This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A181469 #37 Oct 02 2022 20:09:05
%S A181469 88,90,177,179,266,355,533,535,622,624,711,713,800,802,889,1067,1156,
%T A181469 1158,1247,1334,1423,1425,1601,1781,1959,2224,2313,2402,2404,2491,
%U A181469 2493,2582,2669,2849,3025,3381,3383,3739,3826,4093,4095,4184,4271,4451,4716
%N A181469 Numbers n such that 89 is the largest prime factor of n^2-1.
%C A181469 Sequence is finite, for proof see A175607.
%C A181469 Search for terms can be restricted to the range from 2 to A175607(24) = 332110803172167361; primepi(89) = 24.
%H A181469 Lucas A. Brown, <a href="/A181469/b181469.txt">Table of n, a(n) for n = 1..2371</a> (terms 1..432 and 434..2371 from _Artur Jasinski_, term 433 from _Lucas A. Brown_, Oct 01 2022. This is the complete list of terms assuming an abc conjecture c < rad(abc)^2).
%H A181469 From _David A. Corneth_, Oct 02 2022: (Start)
%H A181469 To verify full I listed all 89-smooth numbers k that are a multiple of 89 below (inclusive) A175607(24) + 2. I then checked if k+2 is 89-smooth. If so, k+1 is a term. Then similarily I checked if k-2 is 89-smooth. If so, k-1 is a term.
%H A181469 Doing so found the 2371 terms from the b-file. All candidates have been checked completing the proof of full. (End)
%t A181469 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 == 89, AppendTo[rr, n]]]; n++ ]; rr (* _Artur Jasinski_ *)
%t A181469 Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==89&]
%o A181469 (Magma) [ n: n in [2..300000] | m eq 89 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // _Klaus Brockhaus_, Feb 21 2011
%o A181469 (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 89 where D is PrimeDivisors(n^2-1)) ]; // _Klaus Brockhaus_, Feb 21 2011
%o A181469 (PARI) is(n)=n=n^2-1; forprime(p=2, 83, n/=p^valuation(n, p)); n>1 && 89^valuation(n, 89)==n \\ _Charles R Greathouse IV_, Jul 01 2013
%Y A181469 Cf. A175607, A181447-A181468, A181470, A181568.
%K A181469 nonn,fini,full
%O A181469 1,1
%A A181469 _Artur Jasinski_, Oct 21 2010