A360767 Numbers k that are neither prime power nor squarefree, such that k/rad(k) < q, where rad(k) = A007947(k) and prime q = A119288(k).

12, 20, 28, 40, 44, 45, 52, 56, 60, 63, 68, 76, 84, 88, 92, 99, 104, 116, 117, 124, 132, 136, 140, 148, 152, 153, 156, 164, 171, 172, 175, 176, 184, 188, 204, 207, 208, 212, 220, 228, 232, 236, 244, 248, 260, 261, 268, 272, 275, 276, 279, 280, 284, 292, 296, 297, 304, 308, 315, 316, 325, 328, 332, 333

Offset: 1

Author

Michael De Vlieger, Feb 28 2023

Keywords

• nonn
• easy

Comments

Proper subsequence of A126706.

Numbers k such that there does not exist j such that 1 < j < k and rad(j) = rad(k), but j does not divide k.

Examples

			a(1) = 12, since 12/6 < 3.
a(2) = 20, since 20/10 < 5.
a(3) = 28, since 28/14 < 7.
a(4) = 40, since 40/10 < 5, etc.
		

Links

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

Crossrefs

Cf. A007947, A013929, A024619, A119288, A126706, A355432, A360768.

Programs

Mathematica

Select[Select[Range[120], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], #1/#2 < #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@ {#, FactorInteger[#][[All, 1]]} &]

PARI

rad(n) = factorback(factorint(n)[, 1]); \\ A007947
f(n) = if (isprimepower(n) || (n==1), 1, my(f=factor(n)[, 1]); f[2]); \\ A119288
isok(k) = !isprimepower(k) && !issquarefree(k) && (k/rad(k) < f(k)); \\ Michel Marcus, Mar 01 2023

Formula

This sequence is { k in A126706 : k/A007947(k) < A119288(k) } = A126706 \ A360768.