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Least integers of their prime signature (A025487) whose average number of distinct prime factors of their divisors is an integer.
2

%I #11 Jun 25 2024 01:29:54

%S 1,6,210,900,1080,1440,30030,69300,83160,110880,5292000,9261000,

%T 9525600,9699690,15315300,18378360,24504480,67737600,170100000,

%U 181440000,244944000,416215800,435456000,554954400,756756000,901800900,1324323000,1362160800,6469693230,6692786100

%N Least integers of their prime signature (A025487) whose average number of distinct prime factors of their divisors is an integer.

%C Since f(k) = A346009(k)/A346010(k), the average number of distinct prime factors of the divisors of k, depends only on the prime signature of k, the sequence A346014 consists of all the numbers with the same prime signature of terms of this sequence.

%H Amiram Eldar, <a href="/A346015/b346015.txt">Table of n, a(n) for n = 1..10000</a>

%t lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; f[p_, e_] := e/(e + 1); d[1] = 1; d[n_] := Denominator[Plus @@ f @@@ FactorInteger[n]]; Select[lps, d[#] == 1 &]

%Y Intersection of A025487 and A346014.

%Y Cf. A346009, A346010.

%K nonn

%O 1,2

%A _Amiram Eldar_, Jul 01 2021