OFFSET
1,1
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..10000
Michael De Vlieger, Plot b(n) = A126706(n) at (x, y) for n = ym + x = 1..1032256, m = 1016 and x = 1..m, y = 0..m-1, showing b(n) in A360765 in white, and b(n) in this sequence in other colors, where red indicates b(n) also in A360767, and blue indicates b(n) also in A360768.
EXAMPLE
a(1) = 12 since 12 is the smallest number that is neither squarefree nor a prime power. Additionally, 12 < 5*6.
a(2) = 18 since it is in A126706, and like 12, 18 < 5*6.
a(3) = 20 since it is neither squarefree nor prime power, and 20 < 3*10.
36 is not in this sequence since 36 > 5*6.
40 is not in this sequence since 40 > 3*10, etc.
MATHEMATICA
Select[Select[Range[452], Nor[PrimePowerQ[#], SquareFreeQ[#]] &], Function[{k, f}, Function[{q, r}, q r > k] @@ {SelectFirst[Prime@ Range[PrimePi[f[[-1, 1]]] + 1], ! Divisible[k, #] &], Times @@ f[[All, 1]]} ] @@ {#, FactorInteger[#]} &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Jul 29 2023
STATUS
approved