A362432 a(n) is the smallest k > A126706(n) such that rad(k) = rad(A126706(n)) and k mod n != 0, where rad(n) = A007947(n).

18, 24, 50, 36, 98, 48, 50, 242, 75, 54, 80, 338, 72, 98, 90, 147, 578, 96, 135, 722, 100, 126, 242, 120, 1058, 108, 112, 363, 160, 338, 144, 196, 1682, 507, 150, 1922, 168, 198, 225, 578, 350, 162, 189, 2738, 180, 722, 867, 234, 200, 192, 3362, 252, 1083, 3698, 245, 242, 240, 1058, 4418, 441, 216, 224

Offset: 1

Author

Michael De Vlieger, May 19 2023

Keywords

• nonn

Comments

Let m = A126706(n) and r = rad(m).

Smallest number k greater than m that shares the same squarefree kernel as m, yet does not divide m.

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

k/r and m/r are coprime.

a(n) < m^2, since k/m < r.

Examples

			A126706(1) = 12; the smallest k > 12 such that both rad(k) = rad(12) = 6 and 12 does not divide k is a(1) = 18.
A126706(2) = 18; the smallest k > 18 such that both rad(k) = rad(18) = 6 and 18 does not divide k is a(2) = 24.
A126706(3) = 20; the smallest k > 20 such that rad(k) = rad(20) = 10, indivisible by 20, is a(3) = 50.
A126706(7) = 40; the smallest k > 40 such that rad(k) = rad(40) = 10, indivisible by 40, is a(7) = 50.
		

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, A065642, A126706.

Programs

Mathematica

rad[x_] := rad[x] = Times @@ FactorInteger[x][[All, 1]]; Table[k = m + 1; Function[r, While[Nand[rad[k] == r, ! Divisible[k, m]], k++]][rad[m]]; k, {m, Select[Range[196], Nor[PrimePowerQ[#], SquareFreeQ[#]] &]}]