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A346016
Numbers k where the average number of distinct prime factors of the divisors of k sets a new record.
2
1, 2, 4, 6, 12, 24, 30, 60, 120, 180, 210, 420, 840, 1260, 2310, 4620, 9240, 13860, 27720, 30030, 60060, 120120, 180180, 360360, 510510, 1021020, 2042040, 3063060, 6126120, 9699690, 19399380, 38798760, 58198140, 116396280, 223092870, 446185740, 892371480, 1338557220
OFFSET
1,2
COMMENTS
First differs from A282472 at n = 48.
The corresponding record values are 0, 1/2, 2/3, 1, 7/6, 5/4, 3/2, 5/3, 7/4, 11/6, 2, ...
All the terms are least integers of their prime signature (A025487) since f(n) = A346009(n)/A346010(n) depends only on the prime signature of n.
This sequence is infinite since f(n) is unbounded. E.g., f(A002110(n)) = n/2.
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 = {}; fmax = -1; Do[f1 = f[lps[[k]]]; If[f1 > fmax, fmax = f1; AppendTo[s, lps[[k]]]], {k, 1, Length[lps]}]; s
CROSSREFS
Subsequence of A025487.
Sequence in context: A340816 A168264 A282472 * A368252 A095416 A056795
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 01 2021
STATUS
approved