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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
1, 6, 210, 30030, 9699690, 6469693230, 6016814703900, 9127507905816300, 18446693477654742300, 57682810504626379172100, 235749646532408011676372700, 1221890417977470724518639704100, 8011935470678275540668720539783700, 69167038918365552742593064419952682100
OFFSET
0,2
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
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
CROSSREFS
Subsequence of A025487, A346014 and A346015.
Sequence in context: A028350 A359761 A238685 * A099788 A126676 A073100
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 01 2021
STATUS
approved