OFFSET
1,1
COMMENTS
A divisor of a number k is coreful if it is divisible by every prime that divides k.
The sequence is restricted to nonsquarefree numbers since the squarefree numbers have a single coreful divisor and thus they trivially have an integer harmonic mean.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
EXAMPLE
12 is a term since its coreful divisors are 6 and 12 and their harmonic mean, 8, is an integer.
MATHEMATICA
rad[n_] := Times @@ FactorInteger[n][[;; , 1]]; corHarmQ[n_] := Module[{r = rad[n], d}, d = Select[Divisors[n], rad[#] == r &]; IntegerQ[HarmonicMean[d]]]; Select[Range[10^3], !SquareFreeQ[#] && corHarmQ[#] &]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Nov 09 2021
STATUS
approved