A346017 a(n) is the least number k such that the average number of distinct prime factors of the divisors of k is equal to n.

1, 6, 210, 30030, 9699690, 6469693230, 6016814703900, 9127507905816300, 18446693477654742300, 57682810504626379172100, 235749646532408011676372700, 1221890417977470724518639704100, 8011935470678275540668720539783700, 69167038918365552742593064419952682100

Offset: 0

Author

Amiram Eldar, Jul 01 2021

Keywords

• nonn

Comments

This sequence is well-defined since for each n there are infinitely many numbers k such that f(k) = A346009(k)/A346010(k) = n. E.g., if k is a squarefree number (A005117) with 2*n prime factors, then f(k) = n.

All the terms are least integers of their prime signature (A025487) since f(n) depends only on the prime signature of n.

Links

• Amiram Eldar, Table of n, a(n) for n = 0..16

Crossrefs

Cf. A005117, A346009, A346010.

Subsequence of A025487, A346014 and A346015.

Programs

Mathematica

lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {, }][[;; , 2]]; f[p_, e_] := e/(e + 1); f[1] = 0; f[n_] := Plus @@ f @@@ FactorInteger[n]; s = Table[0, {7}]; Do[n = lps[[k]]; f1 = f[n]; If[IntegerQ[f1] && s[[f1+1]] == 0, s[[f1+1]] = n], {k, 1, Length[lps]}]; s