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Numbers whose cubes have more square divisors than the cube of any smaller number.
1

%I #10 Oct 18 2024 20:27:12

%S 1,2,4,8,12,24,36,72,144,180,360,720,900,1800,3600,6300,10800,12600,

%T 25200,44100,75600,88200,176400,352800,529200,705600,1411200,1587600,

%U 1940400,3880800,5821200,7761600,15523200,17463600,21344400,42688800,64033200,85377600,170755200

%N Numbers whose cubes have more square divisors than the cube of any smaller number.

%C Indices of records in A092520.

%C The corresponding record values are 1, 2, 4, 5, 8, 10, 16, 20, 28, 32, 40, 56, 64, 80, 112, 128, ... (see the link for more values).

%H Amiram Eldar, <a href="/A377141/b377141.txt">Table of n, a(n) for n = 1..355</a>

%H Amiram Eldar, <a href="/A377141/a377141.txt">Table of n, a(n), A363825(a(n)) for n = 1..355</a>

%t f[p_, e_] := Floor[(3*e+2)/2]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n]; With[{v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]}, seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq]

%Y Subsequence of A025487.

%Y Cf. A092520.

%K nonn

%O 1,2

%A _Amiram Eldar_, Oct 17 2024