A346015 Least integers of their prime signature (A025487) whose average number of distinct prime factors of their divisors is an integer.

1, 6, 210, 900, 1080, 1440, 30030, 69300, 83160, 110880, 5292000, 9261000, 9525600, 9699690, 15315300, 18378360, 24504480, 67737600, 170100000, 181440000, 244944000, 416215800, 435456000, 554954400, 756756000, 901800900, 1324323000, 1362160800, 6469693230, 6692786100

Offset: 1

Author

Amiram Eldar, Jul 01 2021

Keywords

• nonn

Comments

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.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A025487 and A346014.

Cf. A346009, A346010.

Programs

Mathematica

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 &]