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%I #8 Apr 19 2023 19:00:38
%S 48,125,224,243,567,512,832,960,1331,2048,1715,2048,2187,1792,2944,
%T 4131,3125,4617,3712,3968,8125,4374,5589,5000,8192,9317,6144,8192,
%U 10625,8192,19683,15379,19683,12032,11875,11016,11907,13568,12500,19683,13122,14375,15104,16807,15616,19683,19683,17576,45619
%N a(n) = smallest k such that k > m^2 and rad(k) | m, where rad(k) = A007947(k) and m = A120944(n).
%C The smallest k such that k > p^2 such that p is prime and rad(k) | p is p^3.
%H Michael De Vlieger, <a href="/A362045/b362045.txt">Table of n, a(n) for n = 1..32768</a>
%H Michael De Vlieger, <a href="/A362045/a362045.png">Scatterplot of a(n), m^2, and b(n)</a>, n = 1..2^14, where b(n) = A362044(n) is shown in blue, m^2 in black, and a(n) in red.
%e a(1) = 48 since m = 6 and the smallest k > m^2 such that rad(k) | 6 is 48. This is to say, the number that follows 6^2 in A003586 is 48.
%e a(2) = 80 since m = 10 and the smallest k > m^2 such that rad(k) | 10 is 125. This is to say, the number that precedes 10^2 in A003592 is 125.
%e Table of n = 1..12, m = A120944(n), m^2, and a(n).
%e n m m^2 a(n)
%e ---------------------
%e 1 6 36 48
%e 2 10 100 125
%e 3 14 196 224
%e 4 15 225 243
%e 5 21 441 567
%e 6 22 484 512
%e 7 26 676 832
%e 8 30 900 960
%e 9 33 1089 1331
%e 10 34 1156 2048
%e 11 35 1225 1715
%e 12 38 1444 2048
%t Table[m = k^2 + 1; While[! Divisible[k, Times @@ FactorInteger[m][[All, 1]]], m++]; m, {k, Select[Range[6, 133], And[CompositeQ[#], SquareFreeQ[#]] &]}]
%Y Cf. A007947, A120944, A289280, A362044.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Apr 05 2023
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