A349180 - OEIS

%I #9 Nov 16 2021 01:21:51

%S 12,18,36,56,60,75,84,90,126,132,150,156,168,180,198,204,228,234,240,

%T 252,276,280,306,342,348,351,372,392,396,414,420,444,450,468,492,504,

%U 516,522,525,558,564,588,612,616,630,636,660,666,684,702,708,720,726,728

%N Coreful harmonic numbers: nonsquarefree numbers k such that the harmonic mean of the coreful divisors of k is an integer.

%C A divisor of a number k is coreful if it is divisible by every prime that divides k.

%C 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.

%H Amiram Eldar, <a href="/A349180/b349180.txt">Table of n, a(n) for n = 1..10000</a>

%e 12 is a term since its coreful divisors are 6 and 12 and their harmonic mean, 8, is an integer.

%t 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[#] &]

%Y Cf. A005117, A013929, A057723, A307958, A307959.

%Y Similar sequences: A001599, A006086, A063947, A286325, A319745, A348964.

%K nonn

%O 1,1

%A _Amiram Eldar_, Nov 09 2021