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 A378179 #12 Nov 27 2024 18:35:16
%S A378179 19,51,53,55,89,91,97,149,151,161,163,197,199,233,235,241,249,251,269,
%T A378179 271,293,295,305,307,337,339,341,349,377,379,413,415,449,451,485,487,
%U A378179 489,491,521,523,551,557,559,577,579,593,595,629,631,638,649,651,665,667
%N A378179 Squarefree numbers k whose neighbors are neither squarefree nor prime powers.
%H A378179 Michael De Vlieger, <a href="/A378179/b378179.txt">Table of n, a(n) for n = 1..10000</a>
%e A378179 Numbers k < 12 are not in the sequence since 12 is the smallest number in A126706.
%e A378179 13 and 15 are not in the sequence since 14 is squarefree.
%e A378179 17 is not in the sequence since 16 = 2^4.
%e A378179 a(1) = 19 since 19 is the smallest squarefree number such that 18 = 2*3^2 and 20 = 2*5^2 are not prime powers, but are divisible by a prime square.
%e A378179 a(2) = 51 since 50 = 2*5^2 and 52 = 2^2*13.
%e A378179 a(3) = 53 since 54 = 2*3^3.
%e A378179 a(4) = 55 since 56 = 7*2^3.
%e A378179 a(5) = 89 since 88 = 2^3*11 and 90 = 2*3^2*5, etc.
%t A378179 Reap[Do[If[
%t A378179 And[SquareFreeQ[n],
%t A378179 AllTrue[n + {-1, 1}, Nor[SquareFreeQ[#], PrimePowerQ[#]] &]],
%t A378179 Sow[n]], {n, 1000}] ][[-1, 1]]
%o A378179 (PARI) list(lim)=my(v=List(),l1,l2); forfactored(k=18,lim\1+1, if(!issquarefree(k) && !issquarefree(l2) && issquarefree(l1) && #k[2][,1]>1 && #l2[2][,1]>1, listput(v,l1[1])); l2=l1; l1=k); Vec(v) \\ _Charles R Greathouse IV_, Nov 27 2024
%Y A378179 Subsequence of A073247.
%Y A378179 Cf. A005117, A013929, A024619, A126706.
%K A378179 nonn,easy
%O A378179 1,1
%A A378179 _Michael De Vlieger_, Nov 24 2024