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A374907
Number whose divisors have a mean number of divisors that attains a record value.
2
1, 2, 4, 6, 8, 12, 24, 36, 48, 72, 96, 120, 144, 216, 240, 288, 360, 480, 576, 720, 1080, 1440, 2160, 2880, 4320, 5040, 7200, 7560, 8640, 10080, 14400, 15120, 20160, 30240, 40320, 50400, 60480, 90720, 100800, 120960, 151200, 181440, 241920, 302400, 362880, 453600
OFFSET
1,2
COMMENTS
First differs from A301414 at n = 454: a(454) = 526399743264198303532032000 is not a term of A301414. Is A301414 a subsequence of this sequence? The first 1073 terms of A301414 are in this sequence.
Indices of records of A374902(k)/A374903(k) = A007425(k)/A000005(k).
All the terms are least integers of their prime signature (A025487) since A374902(k)/A374903(k) depends only on the prime signature of k.
The corresponding record values are 1, 3/2, 2, 9/4, 5/2, 3, 15/4, 4, 9/2, 5, ... .
LINKS
MATHEMATICA
lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]; f[p_, e_] := e/2 + 1; f[1] = 1; f[n_] := Times @@ 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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 23 2024
STATUS
approved