A362844 a(n) is the largest k < A360768(n) such that rad(k) = rad(A360768(n)) and n mod k != 0, where rad(n) = A007947(n).

12, 18, 24, 36, 40, 48, 54, 45, 50, 60, 72, 56, 80, 96, 98, 90, 84, 75, 108, 63, 120, 100, 144, 126, 150, 147, 162, 112, 132, 160, 192, 196, 135, 156, 180, 176, 175, 200, 168, 198, 240, 216, 252, 270, 204, 234, 250, 288, 294, 208, 228, 280, 242, 300, 297, 225, 336, 324, 224, 264, 320, 375, 306, 276

Offset: 1

Author

Michael De Vlieger, May 19 2023

Keywords

• nonn

Comments

Largest nondivisor less than m = A360768(n) that shares the same squarefree kernel as m.

a(n) is in A126706, not a permutation of A126706.

Examples

			A360768(1) = 18; the smallest nondivisor k < 18 such that rad(k) = rad(18) = 6 is a(1) = 12.
A360768(2) = 24; the smallest nondivisor k < 24 such that rad(k) = rad(24) = 6 is a(2) = 18.
A360768(5) = 50; the smallest nondivisor k < 50 such that rad(k) = rad(50) = 10 is a(5) = 40.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^12, showing records in red.

Crossrefs

Cf. A007947, A126706, A360768, A362041.

Programs

Mathematica

rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; s = Select[Select[Range[414],  Nor[SquareFreeQ[#], PrimePowerQ[#]] &], #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@ {#, FactorInteger[#][[All, 1]]} &]; Table[Function[r, SelectFirst[Range[m - 1, 1, -1], r == rad[#] &] ][rad[m]], {m, s}]