A333961 Numbers k with property that k is the least logarithmically smooth numbers (meaning largest prime factor of k is less than log(k)) having squarefree kernel equal to squarefree kernel of k.

8, 24, 27, 150, 160, 225, 625, 1120, 1134, 1225, 1260, 1323, 1372, 1575, 2401, 59895, 60368, 60500, 60984, 61600, 61952, 62370, 63360, 63525, 63888, 65219, 67375, 68607, 72171, 73205, 161051, 443625, 445900, 446160, 446875, 447174, 448448, 449280, 449878, 450450

Offset: 1

Author

David A. Corneth, Apr 12 2020

Keywords

• nonn

Comments

Primitive sequence underlying A137845. If k is in this sequence then any number larger than k having the same squarefree kernel is in the sequence.

Examples

			8 is in the sequence as the largest prime factor of 8 is 2 and log(8) > 2 and 8 is the least positive integer with this property and squarefree kernel 2.
		

Crossrefs

Cf. A007947, A137845.

Programs

Mathematica

rads = seq = {}; Do[rad = Times @@ (p = First /@ FactorInteger[n]); pmax = Max[p]; If[pmax < Log[n] && ! MemberQ[rads, rad], AppendTo[rads, rad]; AppendTo[seq, n]], {n, 1, 5*10^5}]; seq (* Amiram Eldar, Apr 12 2020 *)