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 A355709 #10 Jul 19 2022 08:02:48
%S A355709 2,14,21,33,38,44,50,57,69,74,80,86,93,99,105,110,116,122,129,135,141,
%T A355709 146,158,165,171,177,182,194,201,213,218,230,237,249,254,260,266,273,
%U A355709 285,290,296,302,309,315,321,326,332,338,345,357,362,374,381,387,393,398
%N A355709 Numbers k such that k and k+1 have the same number of 3-smooth divisors.
%C A355709 Numbers k such that A072078(k) = A072078(k+1).
%C A355709 This sequence is infinite since it includes all the numbers of the form 3*(2^(2*k+1)-1), with k>=1.
%H A355709 Amiram Eldar, <a href="/A355709/b355709.txt">Table of n, a(n) for n = 1..10000</a>
%e A355709 2 is a term since A072078(2) = A072078(3) = 2.
%t A355709 s[n_] := Times @@ (1 + IntegerExponent[n, {2, 3}]); Select[Range[400], s[#] == s[#+1] &]
%o A355709 (PARI) s(n) = (valuation(n, 2) + 1) * (valuation(n, 3) + 1);
%o A355709 s1 = s(1); for(k = 2, 400, s2 = s(k); if(s1 == s2, print1(k-1,", ")); s1 = s2);
%Y A355709 Cf. A072078, A355710 (5-smooth analog).
%Y A355709 Similar sequences: A005237, A006049, A332386, A343819, A344312, A344313, A344314, A348345.
%K A355709 nonn
%O A355709 1,1
%A A355709 _Amiram Eldar_, Jul 15 2022