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 A342031 #11 Mar 08 2021 03:28:22
%S A342031 1,16,241,2644,4372,1431124,12502348,112753348,750031648,2844282247,
%T A342031 5882272324,6741230497,8004453748,87346072024,130489991521,
%U A342031 218551872247,245127093748,460925878624,804065433748,1176638279524,2210511903748,2404792968748,2483167488748,3121595927521
%N A342031 Starts of runs of 5 consecutive numbers that have mutually distinct exponents in their prime factorization (A130091).
%C A342031 Bernardo Recamán Santos (2015) showed that there is no run of more than 23 consecutive numbers, since numbers of the form 36*k - 6 and 36*k + 6 do not have distinct exponents. Pace Nielsen and _Adam P. Goucher_ showed that there can be only finitely many runs of 23 consecutive numbers (see MathOverflow link).
%C A342031 Aktaş and Ram Murty (2017) gave an explicit upper bound to such a run of 23 numbers. They found the first 5 terms of this sequence (and stated that there are a few more known up to 7*10^8), and said that we may conjecture (based on numerical evidence) that there are no 6 consecutive numbers.
%H A342031 Martin Ehrenstein, <a href="/A342031/b342031.txt">Table of n, a(n) for n = 1..43</a>
%H A342031 Kevser Aktaş and M. Ram Murty, <a href="https://doi.org/10.1007/s12044-016-0326-z">On the number of special numbers</a>, Proceedings - Mathematical Sciences, Vol. 127, No. 3 (2017), pp. 423-430; <a href="https://www.ias.ac.in/article/fulltext/pmsc/127/03/0423-0430">alternative link</a>.
%H A342031 Bernardo Recamán Santos, <a href="http://mathoverflow.net/questions/201489">Consecutive numbers with mutually distinct exponents in their canonical prime factorization</a>, MathOverflow, Mar 30 2015.
%e A342031 16 is a term since 16 = 2^4, 17, 18 = 2*3^2, 19 and 20 = 2^2*5 all have distinct exponents in their prime factorization.
%t A342031 q[n_] := Length[(e = FactorInteger[n][[;; , 2]])] == Length[Union[e]]; v = q /@ Range[5]; seq = {}; Do[If[And @@ v, AppendTo[seq, k - 5]]; v = Join[Rest[v], {q[k]}], {k, 6, 1.3*10^6}]; seq
%Y A342031 Subsequence of A130091, A342028, A342029 and A342030.
%K A342031 nonn
%O A342031 1,2
%A A342031 _Amiram Eldar_, Feb 25 2021
%E A342031 a(15) and beyond from _Martin Ehrenstein_, Mar 08 2021