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.
a(2) = 3; 3^2 + 1 = 2 * 5. a(3) = 13; 13^3 + 1 = 2 * 7 * 157. a(4) = 43; 43^4 + 1 = 2 * 17 * 193 * 521.
a(n) = my(p=2); while (!issquarefree(p^n+1) || omega(p^n+1) != n, p = nextprime(p+1)); p;
a(1) = 5; 5^1 + 6 = 11. a(2) = 2; 2^2 + 6 = 2 * 5. a(3) = 23; 23^3 + 6 = 7 * 37 * 47. a(4) = 127; 127^4 + 6 = 7 * 131 * 367 * 773.
Table[b=6;y[a_]:=FactorInteger[Prime[a]^n+b];k=1;Monitor[Parallelize[While[True,If[And[Length[y[k]]==n,Count[Flatten[y[k]],1]==n],Break[]];k++];k],k]//Prime,{n,1,10}]
a(n) = forprime(p=2, , my(f=factor(p^n + 6)); if (issquarefree(f) && (omega(f) == n), return(p)));
a(5) = 7 is the smallest number of the set {k(i)} = {7, 14, 24, 26, 46, 51, ...} where k(i)^5 + 1 has exactly 5 prime factors counted with multiplicity.
a(n) = my(k=1); while (bigomega(k^n+1) != n, k++); k;
a(3) = 5 is the smallest prime of the set {p(i)} = {5, 11, 13, 19, 23, ...} where omega(p(i)^3 + 1) = 3.
a[n_] := Module[{p = 2}, While[PrimeNu[p^n + 1] != n, p = NextPrime[p]]; p]; Print[Array[a, 11]]
a(n) = forprime(p=2, oo, if(omega(p^n+1) == n, return(p)));
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