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 A364702 #7 Aug 05 2023 21:33:01
%S A364702 48,50,54,75,80,96,98,112,135,147,160,162,189,192,224,240,242,245,250,
%T A364702 252,270,294,300,320,336,338,350,352,360,363,375,378,384,396,405,416,
%U A364702 448,450,468,480,486,490,504,507,525,528,540,550,560,567,578,588,594,600
%N A364702 Numbers k in A361098 that are not divisible by A007947(k)^2.
%C A364702 Subset of A126706, the set of numbers k neither prime powers nor squarefree, i.e., k such that A001222(k) > A001221(k) > 1.
%C A364702 Let p = A119288(k) be the second smallest prime factor of k. Let q = A053669(k) be the smallest prime that does not divide k. Let r = rad(k) = A007947(k) be the squarefree kernel of k. Define sequence S = A361098 = {k : Omega(k) > omega(k) > 1, q*r < k, p*r <= k} = A361098.
%C A364702 Sequence T = A286708 represents numbers in A001694 that are not prime powers. Numbers k in T are such that k = m*r^2, m >= 1, by definition. Since we may rewrite q*r < k instead as q*r < m*r^2, it is clear since omega(r) > 1, that q < r. Further, we may rewrite p*r <= k instead as p*r <= m*r^2, and since p | r, p < r as omega(r) > 1, we see that S contains T.
%C A364702 This sequence gives k that are in S but not in T.
%H A364702 Michael De Vlieger, <a href="/A364702/b364702.txt">Table of n, a(n) for n = 1..10000</a>
%F A364702 This sequence is A361098 \ A286708.
%e A364702 Let B = A126706.
%e A364702 B(1) = 12 is not in the sequence since 3*6 > 12.
%e A364702 B(2) = 18 is not in the sequence, since, though 3*6 = 18, 5*6 > 18.
%e A364702 B(6) = S(1) = 36 is not in the sequence since, though 3*6 < 36 and 5*6 < 36, rad(36)^2 = 6^2 | 36, hence B(6) = T(1).
%e A364702 B(10) = S(2) = a(1) = 48 is in the sequence since rad(48) = 6, and 6^2 does not divide 48.
%e A364702 B(11) = S(3) = a(2) = 50 is in the sequence since rad(50) = 10, and 10^2 does not divide 50, etc.
%t A364702 nn = 2^10; a053669[n_] := If[OddQ[n], 2, p = 2; While[Divisible[n, p], p = NextPrime[p]]; p]; s = Select[Range[nn], Nor[PrimePowerQ[#], SquareFreeQ[#]] &]; Reap[Do[n = s[[j]]; If[And[#1*a053669[n] < n, #1*#2 <= n, ! Divisible[n, #1^2]] & @@ {Times @@ #, #[[2]]} &@ FactorInteger[n][[All, 1]], Sow[n]], {j, Length[s]}] ][[-1, -1]]
%Y A364702 Cf. A001221, A001222, A001694, A007947, A053669, A119288, A126706, A286708, A361098.
%K A364702 nonn
%O A364702 1,1
%A A364702 _Michael De Vlieger_, Aug 03 2023