A370266 Numbers k that are not prime powers, such that k/rad(k) >= rad(k), where rad(k) = A007947(k).

36, 48, 54, 72, 96, 100, 108, 144, 160, 162, 192, 196, 200, 216, 224, 225, 250, 288, 320, 324, 375, 384, 392, 400, 405, 432, 441, 448, 484, 486, 500, 567, 576, 640, 648, 675, 676, 686, 704, 768, 784, 800, 832, 864, 896, 900, 960, 968, 972, 1000, 1029, 1080, 1089

Offset

1,1

Comments

Numbers k = m * s, where s is composite and squarefree, rad(m) | s, and m >= s.

A177492 is a proper subset.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Formula

Set difference of A341645 and A246547.

Intersection of A341645 and A126706.

Union of A286708 and A366250.

Example

For s = 6, this sequence contains {36, 48, 54, 72, 96, ...}, i.e., A033845(n) for n >= A010846(6).
For s = 10, this sequence contains {100, 160, 200, 250, 320, ...}, i.e., A033846(n) for n >= A010846(10).
For s = 14, this sequence contains {196, 224, 392, 448, 686, ...}, i.e., A033847(n) for n >= A010846(14).
For s = 15, this sequence contains {225, 375, 405, 675, 1125, ...}, i.e., A033849(n) for n >= A010846(15), etc.

Mathematica

Select[Select[Range[2, 1100], Not@*PrimePowerQ], #1/#2 >= #2 & @@ {#, Times @@ FactorInteger[#][[All, 1]]} &]

Crossrefs

Cf. A007947, A010846, A024619, A120944, A126706, A177492, A246547, A286708, A341645, A366250.

Sequence in context: A260927 A361098 A291713 * A287840 A244326 A357605

Adjacent sequences: A370263 A370264 A370265 * A370267 A370268 A370269

Keyword

nonn,easy

Author

Michael De Vlieger, Feb 18 2024

Status

approved