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 A181466 #19 Dec 21 2024 17:59:13
%S A181466 72,74,145,147,218,220,291,293,364,439,512,729,731,804,875,1021,1023,
%T A181466 1167,1169,1240,1313,1315,1459,1461,1607,1678,1680,1751,1826,1899,
%U A181466 2045,2116,2262,2481,2483,2554,2702,2773,2848,3067,3284,3359,3576,3649,3722
%N A181466 Numbers k such that 73 is the largest prime factor of k^2 - 1.
%C A181466 Numbers k such that A076605(k) = 73.
%C A181466 Sequence is finite, for proof see A175607.
%C A181466 Search for terms can be restricted to the range from 2 to A175607(21) = 4573663454608289; primepi(73) = 21.
%H A181466 Artur Jasinski, <a href="/A181466/b181466.txt">Table of n, a(n) for n = 1..1439</a>
%t A181466 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 == 73, AppendTo[rr, n]]]; n++ ]; rr (* _Artur Jasinski_ *)
%t A181466 Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==73&]
%o A181466 (Magma) [ n: n in [2..300000] | m eq 73 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // _Klaus Brockhaus_, Feb 21 2011
%o A181466 (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 73 where D is PrimeDivisors(n^2-1)) ]; // _Klaus Brockhaus_, Feb 21 2011
%o A181466 (PARI) is(n)=n=n^2-1; forprime(p=2, 71, n/=p^valuation(n, p)); n>1 && 73^valuation(n, 73)==n \\ _Charles R Greathouse IV_, Jul 01 2013
%Y A181466 Row 21 of A223701
%Y A181466 Cf. A076605, A175607, A181447-A181465, A181467-A181470, A181568.
%K A181466 fini,full,nonn
%O A181466 1,1
%A A181466 _Artur Jasinski_, Oct 21 2010