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Number whose divisors have a mean number of divisors that attains a record value.
2

%I #6 Jul 23 2024 20:47:36

%S 1,2,4,6,8,12,24,36,48,72,96,120,144,216,240,288,360,480,576,720,1080,

%T 1440,2160,2880,4320,5040,7200,7560,8640,10080,14400,15120,20160,

%U 30240,40320,50400,60480,90720,100800,120960,151200,181440,241920,302400,362880,453600

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

%C 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.

%C Indices of records of A374902(k)/A374903(k) = A007425(k)/A000005(k).

%C All the terms are least integers of their prime signature (A025487) since A374902(k)/A374903(k) depends only on the prime signature of k.

%C The corresponding record values are 1, 3/2, 2, 9/4, 5/2, 3, 15/4, 4, 9/2, 5, ... .

%H Amiram Eldar, <a href="/A374907/b374907.txt">Table of n, a(n) for n = 1..1085</a>

%t 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

%Y Subsequence of A025487.

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

%K nonn

%O 1,2

%A _Amiram Eldar_, Jul 23 2024