OFFSET
1,1
COMMENTS
Proper subsequence of A126706.
Numbers k such that there exists j such that 1 < j < k and rad(j) = rad(k), but j does not divide k.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, 1016 pixel square bitmap of indices n = 1..1032256, read left to right, top to bottom, such that A126706(n) in this sequence appears in black and A126706(n) in A360767 in white. Shows a curious "sand ripple" pattern perhaps associated with congruence. (Magnification 3X)
Michael De Vlieger, 1016 pixel square bitmap as described above, at scale 1X.
EXAMPLE
a(1) = 18, since 18/6 >= 3. We note that rad(12) = rad(18) = 6, yet 12 does not divide 18.
a(2) = 24, since 24/6 >= 3. Note: rad(18) = rad(24) = 6 and 24 mod 18 = 6.
a(3) = 36, since 36/6 >= 3. Note: rad(24) = rad(36) = 6 and 36 mod 24 = 12.
a(6) = 54, since 54/6 >= 3. Note: m in {12, 24, 36, 48} are such that rad(m) = rad(54) = 6, but none divides 54, etc.
MATHEMATICA
Select[Select[Range[120], Nor[SquareFreeQ[#], PrimePowerQ[#]] &], #1/#2 >= #3 & @@ {#1, Times @@ #2, #2[[2]]} & @@ {#, FactorInteger[#][[All, 1]]} &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Feb 22 2023
STATUS
approved