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

Author

Michael De Vlieger, Sep 22 2024

Keywords

• nonn

Comments

The term prime power used here refers to k in A246547.

Includes m such that the largest k = A373736(m) in row m of A272618 is not in A246547.

Subset of A024619, since for prime powers m = p^e, e >= 1, all k <= m such that rad(k) | m also divide m.

Contains A376422, since nondivisor k such that rad(k) | m must be composite, and composite prime powers m in A246547 are a subset of A001694.

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

Crossrefs

Cf. A024619, A007947, A246547, A272618, A373736, A376422.

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}]