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 A381063 #9 Feb 22 2025 21:30:28 %S A381063 1,2,3,5,7,8,11,13,17,18,19,23,29,31,37,41,43,47,50,53,59,61,67,71,73, %T A381063 79,83,89,97,98,101,103,107,109,113,127,131,137,139,149,151,157,163, %U A381063 167,173,176,179,181,191,193,197,199,211,223,227,229,233,239,241,251 %N A381063 Lexicographically earliest sequence of positive integers such that each nonempty subset has a distinct geometric mean. %C A381063 Every prime occurs in the sequence. %o A381063 (PARI) is(v, w, k) = my(f=factor(k), x, y, z); for(i=1, #f~, if(setsearch(v, f[i, 1]), listput(w, f[i, 1]))); w=Set(w); forsubset(#w, r, x=#r; y=k*prod(i=1, x, w[r[i]]); forsubset(#w, s, z=#s; if(y^z==prod(i=1, z, w[s[i]])^(x+1)&&z>0, return(0)))); 1; %o A381063 lista(nn) = my(f, k=1, v=[1], w=List([1])); for(n=2, nn, while(!isprime(k++), if(is(v, w, k), f=factor(k); for(i=1, #f~, if(setsearch(v, f[i, 1]), listput(w, f[i, 1]))); listput(w, k); break)); v=concat(v, k)); v; \\ _Jinyuan Wang_, Feb 13 2025 %Y A381063 Cf. A066720, A260873. %K A381063 nonn %O A381063 1,2 %A A381063 _Neal Gersh Tolunsky_, Feb 12 2025 %E A381063 More terms from _Jinyuan Wang_, Feb 13 2025