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A362044
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a(n) = largest k such that k < m^2 and rad(k) | m, where rad(k) = A007947(k) and m = A120944(n).
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2
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32, 80, 128, 135, 343, 352, 512, 864, 891, 1088, 875, 1216, 1053, 1728, 2048, 2187, 1375, 2187, 2048, 2048, 3125, 4224, 2187, 4802, 4736, 3773, 5832, 5248, 4913, 5504, 7047, 4459, 7533, 8192, 6859, 10368, 10935, 8192, 11264, 8991, 12312, 12167, 8192, 5831, 8192, 9963, 10449, 16640, 16807, 17152, 18432
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OFFSET
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1,1
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COMMENTS
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The largest k such that k < p^2 such that p is prime and rad(k) | p is p itself.
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LINKS
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EXAMPLE
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a(1) = 32 since m = 6 and the largest k < m^2 such that rad(k) | 6 is 32. This is to say, the number that precedes 6^2 in A003586 is 32.
a(2) = 80 since m = 10 and the largest k < m^2 such that rad(k) | 10 is 80. This is to say, the number that precedes 10^2 in A003592 is 80.
Table of n = 1..12, m = A120944(n), a(n), and m^2.
n m a(n) m^2
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1 6 32 36
2 10 80 100
3 14 128 196
4 15 135 225
5 21 343 441
6 22 352 484
7 26 512 676
8 30 864 900
9 33 891 1089
10 34 1088 1156
11 35 875 1225
12 38 1216 1444
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MATHEMATICA
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Table[m = k^2 - 1; While[! Divisible[k, Times @@ FactorInteger[m][[All, 1]]], m--]; m, {k, Select[Range[6, 133], And[CompositeQ[#], SquareFreeQ[#]] &]}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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