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 A245569 #31 Nov 28 2014 14:55:50
%S A245569 0,1,2,3,4,6,11,12,21,28,29,31,51,54,55,57
%N A245569 Numbers n such that binomial(2^n-1,n) is squarefree.
%C A245569 Motivated by the previously existing entry for the subsequence A246699 of squarefree terms in this sequence.
%C A245569 Conjectured to be finite. Next term, if it exists, is larger than 500.
%t A245569 Select[Range[0,57],SquareFreeQ[Binomial[2^#-1,#]]&] (* _Ivan N. Ianakiev_, Nov 18 2014 *)
%o A245569 (PARI) is(n)=issquarefree(binomial(2^n-1,n))
%o A245569 (PARI) is(n)={t=1; n&&n=vecsort(concat(vector(n,k,factor(if(k<n,numerator,x->x)(t=(2^n-k)/k/denominator(t)),0)~))); for(i=2,#n,if(n[1,i]==n[1,i-1],n[2,i]+=n[2,i-1];n[2,i-1]=0));!n||vecmax(n[2,])<2} \\ Limiting "factor" to precomputed primes might yield a false positive, but no term > 57 is found so far.
%Y A245569 Cf. A000225, A005117, A136556.
%K A245569 nonn,more
%O A245569 1,3
%A A245569 _M. F. Hasler_, Nov 17 2014