This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A384784 #9 Jun 10 2025 08:41:35
%S A384784 1,16,64,256,512,1024,2048,4096,8192,16384,32768,65536,131072,262144,
%T A384784 524288,1048576,2097152,4194304,8388608,16777216,33554432,67108864,
%U A384784 134217728,268435456,536870912,1073741824,2147483648,4294967296,8589934592,17179869184,34359738368
%N A384784 Numbers with a record number of unordered factorizations into 1 and prime powers p^e where p is prime and e >= 2 (A025475).
%C A384784 The least term that is not a power of 2 is a(47) = 2^35 * 3^10.
%C A384784 Indices of records in A188585.
%C A384784 All the terms are powerful numbers since A188585(1) = 1 and A188585(n) = 0 if n is a nonpowerful number.
%C A384784 The corresponding record values are 1, 2, 4, 7, 8, 12, 14, 21, 24, 34, 41, 55, 66, 88, ... (see the link for more values).
%H A384784 Amiram Eldar, <a href="/A384784/b384784.txt">Table of n, a(n) for n = 1..713</a>
%H A384784 Amiram Eldar, <a href="/A384784/a384784.txt">Table of n, a(n), A188585(a(n)) for n = 1..713</a>
%H A384784 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%t A384784 f[p_, e_] := PartitionsP[e] - PartitionsP[e-1]; s[1] = 1; s[n_] := Times @@ f @@@ FactorInteger[n]; With[{lps = Cases[Import["https://oeis.org/A025487/b025487.txt", "Table"], {_, _}][[;; , 2]]}, sm = -1; seq = {}; Do[s1 = s[lps[[i]]]; If[s1 > sm, sm = s1; AppendTo[seq, lps[[i]]]], {i, 1, Length[lps]}]; seq]
%Y A384784 Subsequence of A001694 and A025487 (i.e., of A181800).
%Y A384784 Cf. A025475, A046055, A188585, A384783, A384786 (cubefull analog).
%K A384784 nonn
%O A384784 1,2
%A A384784 _Amiram Eldar_, Jun 10 2025