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%I #12 Apr 06 2023 06:35:46
%S 1,8,216,27000,9261000,12326391000,27081081027000,110924107886592000,
%T 544970142046826496000,3737950204299182936064000,
%U 45479640135708158783090688000,1109202943269786284560798789632000,33044264882950203203350756741926912000,1673791149116076642859325881248823873536000
%N Numbers with a record number of divisors that are both infinitary and exponential.
%C Indices of records in A359411.
%C a(2)-a(7) are the first 6 terms of A115964.
%C The first 15 terms are cubes. Are there noncubes in this sequence?
%C The corresponding record values are 1, 2, 4, 8, 16, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192, ... . Apparently, this sequence of records is the powers of 2 (A000079).
%H Amiram Eldar, <a href="/A359412/b359412.txt">Table of n, a(n) for n = 1..15</a>
%t s[n_] := DivisorSum[n, 1 &, BitAnd[n, #] == # &]; f[p_, e_] := s[e]; d[1] = 1; d[n_] := Times @@ f @@@ FactorInteger[n];
%t v = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]];
%t seq = {}; dm = 0; Do[If[(dk = d[v[[k]]]) > dm, dm = dk; AppendTo[seq, v[[k]]]], {k, 1, Length[v]}]; seq
%Y Cf. A000079, A000578, A115964, A359411.
%Y Subsequence of A025487.
%Y Similar sequences: A037992, A318278.
%K nonn
%O 1,2
%A _Amiram Eldar_, Dec 30 2022
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