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 A260198 #15 Jul 14 2021 01:56:24 %S A260198 49,242,1681,2645,4374,18490,23762,39325,48734,57121,158949,182182, %T A260198 410669,453870,601425,656914,843637,912950,1143449,1228122,1275125, %U A260198 1608574,1940449,2328482,2948406,3041577,3203050,3721549,4495985,4705074,5371029,5606230,6352825 %N A260198 Numbers k such that core(k+1) = core(k)+1 and k is not squarefree, where core(k) = A007913(k). %C A260198 Each term is the first of a consecutive pair of nonsquarefree integers whose cores are consecutive too. %C A260198 If c and c+1 are squarefree, then the sequence contains all the numbers c*x^2 where x is a solution to the Diophantine equation c*x^2+1 = (c+1)*y^2, with x,y > 1, hence the sequence is infinite. %H A260198 Giovanni Resta, <a href="/A260198/b260198.txt">Table of n, a(n) for n = 1..1328</a> (terms < 10^12) %e A260198 182182 is a term, because 182182 = 2*7^2*11*13^2 and 182183 = 23*89^2, so core(182182) = 22 and core(182183) = 23. %t A260198 core[n_] := Times@@ ((#[[1]] ^ Mod[#[[2]], 2]) & /@ FactorInteger@n); Select[ Range[10^5],# != core[#] == core[#+1]-1 &] %Y A260198 Cf. A007913, A007674. %K A260198 nonn %O A260198 1,1 %A A260198 _Giovanni Resta_, Jul 19 2015