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 A342032 #5 Feb 26 2021 04:24:59
%S A342032 1,5,13,32,200,212,1759,2313,5351,16144,51071,128056,159233,630737,
%T A342032 1555349,1627984,2666309,6838261,12243457,14619901,25282087,65891668,
%U A342032 78971281,121377079,543433039,684779072,1675445647,2078471579,2228572121,11135788439,42801667036
%N A342032 Numbers with mutually distinct exponents in their prime factorization (A130091) with a record gap to the next term of A130091.
%C A342032 This sequence is infinite since the asymptotic density of A130091 is 0.
%C A342032 The corresponding values of the record gaps are 1, 2, 3, 5, 7, 11, 13, 20, 22, 29, 33, 40, 51, 55, 59, 67, 72, 82, 84, 87, 100, 121, 126, 132, 138, 147, 149, 150, 195, 209, 211, ...
%e A342032 a(1) = 1 since both 1 and 1+1 = 2 are in A130091.
%e A342032 a(2) = 5 since 5 and 5+2 = 7 are in A130091 and 6 is not.
%e A342032 a(3) = 13 since 13 and 13+3 = 16 are in A130091 and 14 and 15 are not.
%t A342032 q[n_] := Length[(e = FactorInteger[n][[;; , 2]])] == Length[Union[e]]; seq = {}; m = 1; dm = 0; Do[If[q[n], d = n - m; If[d > dm, dm = d; AppendTo[seq, m]]; m = n], {n, 1, 10^6}]; seq
%Y A342032 Cf. A130091, A342028, A342029, A342030, A342031.
%K A342032 nonn
%O A342032 1,2
%A A342032 _Amiram Eldar_, Feb 25 2021