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 A081391 #17 Oct 05 2024 09:11:50
%S A081391 3,6,7,8,9,10,11,12,16,21,22,28,29,30,31,36,37,54,55,57,58,110,171,
%T A081391 784,786
%N A081391 Numbers k such that the central binomial coefficient C(2*k,k) has only one prime divisor whose exponent equals one.
%C A081391 Numbers k such that C(2*k,k) has one non-unitary prime divisor.
%C A081391 Numbers k for which A081387(k) = 1.
%C A081391 No more terms through 10^6; conjecture: no terms after 786. - _Jon E. Schoenfield_, Jul 29 2017
%e A081391 For k = 786, C(1572,786) = 2*2*2*2*m, where m is a squarefree product of 169 primes.
%t A081391 q[k_] := Count[FactorInteger[Binomial[2*k, k]][[;;, 2]], _?( # > 1 &)] == 1; Select[Range[1000], q] (* _Amiram Eldar_, Oct 05 2024 *)
%o A081391 (PARI) is(k) = {my(e = factor(binomial(2*k, k))[, 2]); sum(i = 1, #e, e[i] > 1) == 1;} \\ _Amiram Eldar_, Oct 05 2024
%Y A081391 Cf. A000108, A000984, A001405, A046098, A081386, A081387, A081388, A081389, A081390, A080664.
%K A081391 nonn,more
%O A081391 1,1
%A A081391 _Labos Elemer_, Mar 27 2003