OFFSET
1,1
COMMENTS
Subset of A024619, since for prime powers m = p^e, e >= 1, all k <= m such that rad(k) | m also divide m.
LINKS
Michael De Vlieger, Table of n, a(n) for n = 1..16464
EXAMPLE
6 is not included since nondivisor 4 = 2^2 is such that rad(4) | 6, but 4 is powerful since it is a perfect power of a prime.
24 is included since nondivisor 18 = 2 * 3^2 is such that rad(18) | 24 and is not powerful.
42 is not included since nondivisor 36 = 2^2 * 3^2 is such that rad(36) | 42 but 36 is powerful, since all exponents of prime power factors of 36 exceed 1, i.e., 36 is in A286708, a subset of A001694.
60 is in the sequence because nondivisor 54 = 2 * 3^3 but rad(54) | 60 and 54 is not powerful, etc.
MATHEMATICA
rad[x_] := Times @@ FactorInteger[x][[All, 1]];
Table[If[PrimePowerQ[n], Nothing,
If[! Divisible[#, rad[#]^2], n, Nothing] &@
SelectFirst[Range[n - 1, 1, -1],
And[! Divisible[n, #], Divisible[n, rad[#]]] &] ], {n, 2, 500}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Sep 22 2024
STATUS
approved