A360719 a(n) is the largest k < A126706(n) such that rad(k) = rad(A126706(n)), where rad(n) = A007947(n).

6, 12, 10, 18, 14, 24, 20, 22, 15, 36, 40, 26, 48, 28, 30, 21, 34, 54, 45, 38, 50, 42, 44, 60, 46, 72, 56, 33, 80, 52, 96, 98, 58, 39, 90, 62, 84, 66, 75, 68, 70, 108, 63, 74, 120, 76, 51, 78, 100, 144, 82, 126, 57, 86, 35, 88, 150, 92, 94, 147, 162, 112, 132, 160, 102, 69, 104, 106, 192, 110, 196, 135

Offset: 1

Author

Michael De Vlieger, May 01 2023

Keywords

• nonn

Comments

Permutation of A024619.

Let m = A126706(n) and let R_m be the sequence of numbers k such that rad(k) = rad(m). a(n) gives the predecessor of m in R_m.

Examples

			A126706(1) = 12; the smallest k < 12 such that rad(k) = rad(12) = 6 is a(1) = 6.
A126706(2) = 18; the smallest k < 18 such that rad(k) = rad(18) = 6 is a(2) = 12.
A126706(3) = 20; the smallest k < 20 such that rad(k) = rad(20) = 10 is a(3) = 10.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^16.
• Michael De Vlieger, Log log scatterplot of a(n), n = 1..2^12, showing squarefree numbers in green and highlighting numbers k in A286708 with large light blue dots.

Crossrefs

Cf. A007947, A126706, A360529.

Programs

Mathematica

rad[x_] := Times@ FactorInteger[x][[All, 1]]; Table[Function[r, SelectFirst[Range[m - 1, 1, -1], rad[#] == r &]][rad[m]], {m, Select[Range[225], Nor[SquareFreeQ[#], PrimePowerQ[#]] &]}]