A308912 -id:A308912 - cp's OEIS frontend

A374907 Number whose divisors have a mean number of divisors that attains a record value.

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

Amiram Eldar, Jul 23 2024

nonn

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, ... .

Amiram Eldar, Table of n, a(n) for n = 1..1085

Subsequence of A025487.

Cf. A000005, A002182, A007425, A301414, A308912, A374902, A374903, A374904, A374905, A374906.

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

cp's OEIS Frontend

A374907 Number whose divisors have a mean number of divisors that attains a record value.

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