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.
[ n: n in [2..200] | m eq 5 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 17 2011
Select[Range[200], FactorInteger[#^2-1][[-1, 1]]==5&]
is(n)=n=n^2-1; n>>=valuation(n,2); n/=3^valuation(n,3); n>1 && 5^valuation(n, 5)==n \\ Charles R Greathouse IV, Jul 01 2013
[ n: n in [2..9000] | m eq 7 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 17 2011
Select[Range[9000], FactorInteger[#^2-1][[-1, 1]]==7&]
is(n)=n=n^2-1; forprime(p=2, 5, n/=p^valuation(n, p)); n>1 && 7^valuation(n, 7)==n \\ Charles R Greathouse IV, Jul 01 2013
[ n: n in [2..20000] | m eq 11 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011
Select[Range[20000], FactorInteger[#^2-1][[-1, 1]]==11&]
is(n)=n=n^2-1; forprime(p=2, 7, n/=p^valuation(n, p)); n>1 && 11^valuation(n, 11)==n \\ Charles R Greathouse IV, Jul 01 2013
[ n: n in [2..250000] | m eq 13 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011
Select[Range[250000], FactorInteger[#^2-1][[-1, 1]]==13&]
is(n)=n=n^2-1; forprime(p=2, 11, n/=p^valuation(n, p)); n>1 && 13^valuation(n, 13)==n \\ Charles R Greathouse IV, Jul 01 2013
[ n: n in [2..300000] | m eq 23 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 18 2011
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..10300000] | p mod (n^2-1) eq 0 and (D[#D] eq 23 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 24 2011
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 == 23, AppendTo[rr, n]]]; n++ ]; rr
Select[Range[300000], FactorInteger[#^2-1][[-1, 1]]==23&]
is(n)=n=n^2-1; forprime(p=2, 19, n/=p^valuation(n, p)); n>1 && 23^valuation(n, 23)==n \\ Charles R Greathouse IV, Jul 01 2013
[ n: n in [2..300000] | m eq 31 where m is D[#D] where D is PrimeDivisors(n^2-1) ]; // Klaus Brockhaus, Feb 19 2011
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 31 where D is PrimeDivisors(n^2-1)) ]; // Klaus Brockhaus, Feb 20 2011
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 == 31, AppendTo[rr, n]]]; n++ ]; rr (* Artur Jasinski *)
Select[Range[5000],Max[Transpose[FactorInteger[ #^2-1]][[1]]]==31&] (* Harvey P. Dale, Nov 03 2010 *)
is(n)=n=n^2-1; forprime(p=2, 29, n/=p^valuation(n, p)); n>1 && 31^valuation(n, 31)==n \\ Charles R Greathouse IV, Jul 01 2013
isok(n) = {pfs = factor(n^2-1)[,1]; for (k = 2, n-1, if (factor(k^2-1)[,1] == pfs, return (k));); return (0);}
lista(nn) = {for(n=2, nn, if (k = isok(n), print1(k, ", ");););} \\ Michel Marcus, Nov 04 2013
a(2)=5 because set of prime divisors of 5^2-1 =2^3*3 is {2,3}, the same as for example for 7^2-1 = 2^4*3.
aa = {}; bb = {}; cc = {}; ff = {}; Do[k = n^2 - 1; kk = FactorInteger[k]; b = {}; Do[AppendTo[b, kk[[m]][[1]]], {m, 1, Length[kk]}]; dd = Position[aa, b]; If[dd == {}, AppendTo[cc, n]; AppendTo[aa, b], AppendTo[ff, n]; AppendTo[bb, cc[[dd[[1]][[1]]]]]], {n, 2, 1000000}]; Take[Union[bb,ff],100] (* Artur Jasinski *)
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