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A362045
a(n) = smallest k such that k > m^2 and rad(k) | m, where rad(k) = A007947(k) and m = A120944(n).
3
48, 125, 224, 243, 567, 512, 832, 960, 1331, 2048, 1715, 2048, 2187, 1792, 2944, 4131, 3125, 4617, 3712, 3968, 8125, 4374, 5589, 5000, 8192, 9317, 6144, 8192, 10625, 8192, 19683, 15379, 19683, 12032, 11875, 11016, 11907, 13568, 12500, 19683, 13122, 14375, 15104, 16807, 15616, 19683, 19683, 17576, 45619
OFFSET
1,1
COMMENTS
The smallest k such that k > p^2 such that p is prime and rad(k) | p is p^3.
LINKS
Michael De Vlieger, Scatterplot of a(n), m^2, and b(n), n = 1..2^14, where b(n) = A362044(n) is shown in blue, m^2 in black, and a(n) in red.
EXAMPLE
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.
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.
Table of n = 1..12, m = A120944(n), m^2, and a(n).
n m m^2 a(n)
---------------------
1 6 36 48
2 10 100 125
3 14 196 224
4 15 225 243
5 21 441 567
6 22 484 512
7 26 676 832
8 30 900 960
9 33 1089 1331
10 34 1156 2048
11 35 1225 1715
12 38 1444 2048
MATHEMATICA
Table[m = k^2 + 1; While[! Divisible[k, Times @@ FactorInteger[m][[All, 1]]], m++]; m, {k, Select[Range[6, 133], And[CompositeQ[#], SquareFreeQ[#]] &]}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Apr 05 2023
STATUS
approved