A376421 Numbers m with largest nondivisor k <= m such that rad(k) | m is not a prime power, where rad = A007947.
24, 42, 48, 50, 54, 60, 75, 78, 100, 102, 108, 110, 112, 114, 120, 126, 150, 156, 162, 165, 168, 170, 174, 180, 186, 189, 190, 192, 198, 200, 204, 210, 216, 220, 222, 224, 225, 228, 230, 231, 234, 238, 240, 242, 245, 250, 294, 300, 312, 315, 318, 324, 330, 336
Offset: 1
Keywords
Examples
6 is not included since nondivisor 4 = 2^2 is such that rad(4) | 6, but 4 is a perfect power of a prime. 24 is included since nondivisor 18 = 2 * 3^2 is such that rad(18) | 24 and is not a prime power. 42 is included since nondivisor 36 = 2^2 * 3^2 is such that rad(36) | 42 and 36 is not a prime power. 60 is in the sequence because nondivisor 54 = 2 * 3^3 but rad(54) | 60 and 54 is not a prime power, etc.
Links
- Michael De Vlieger, Table of n, a(n) for n = 1..32299
Programs
-
Mathematica
rad[x_] := Times @@ FactorInteger[x][[All, 1]]; Table[If[PrimePowerQ[n], Nothing, If[PrimePowerQ[#], Nothing, n] &@ SelectFirst[Range[n - 1, 1, -1], And[! Divisible[n, #], Divisible[n, rad[#]]] &] ], {n, 2, 336}]
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