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 A369954 #30 Apr 04 2024 10:01:54
%S A369954 175,245,275,325,425,475,539,575,605,637,725,775,833,845,847,875,925,
%T A369954 931,1025,1075,1127,1175,1183,1225,1325,1375,1421,1445,1475,1519,1525,
%U A369954 1573,1625,1675,1715,1775,1805,1813,1825,1859,1925,1975,2009,2023,2057,2075,2107
%N A369954 Numbers k that are neither squarefree nor prime powers and also coprime to 6.
%C A369954 Define quality Q to signify a number k neither squarefree nor prime power, i.e., k is in A126706. For example, 12 has quality Q but numbers k = 1..11 do not.
%C A369954 Numbers k in this sequence have quality Q and are such that either (k-1) or (k+1) also have quality Q. Hence k also appears in A369276, but not in A369516.
%C A369954 Numbers k such that k mod 12 = 1 or k mod 12 = 5 imply (k-1) in A126706, since 4 divides (k-1).
%C A369954 Numbers k such that k mod 12 = 7 or k mod 12 = 11 imply (k+1) in A126706, since 4 divides (k+1).
%C A369954 Proper subset of A367455.
%C A369954 By definition these odd numbers are such that A053669(k) = 2, therefore A053669(k) < A003557(k), hence this sequence is a proper subset of A360765.
%H A369954 Michael De Vlieger, <a href="/A369954/b369954.txt">Table of n, a(n) for n = 1..10000</a>
%F A369954 Intersection of A007310 and A126706.
%F A369954 Intersection of A007310, A013929, and A024619.
%t A369954 Select[Flatten[Array[6 # + {1, 5} &, 360]], Nor[PrimePowerQ[#], SquareFreeQ[#]] &]
%o A369954 (PARI) isok(k) = !issquarefree(k) && !isprimepower(k) && (gcd(k, 6)==1); \\ _Michel Marcus_, Mar 25 2024
%Y A369954 Cf. A003557, A007310, A008586, A013929, A024619, A053669, A126706, A356322, A369276, A360765, A367455, A369516.
%K A369954 nonn,easy
%O A369954 1,1
%A A369954 _Michael De Vlieger_, Mar 24 2024