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 A384791 #29 Jul 04 2025 19:51:27
%S A384791 1,256,4096,32768,262144,1048576,8388608,16777216,134217728,268435456,
%T A384791 1073741824,4294967296,8589934592,34359738368,68719476736,
%U A384791 110075314176,549755813888,557256278016,1761205026816,4458050224128,7044820107264,8916100448256,56358560858112,71328803586048
%N A384791 Numbers with a record number of ways in which they can be expressed as b^3 * c^4 * d^5, with b, c and d >= 1.
%C A384791 The least term that is not a power of 2 is a(16) = 2^24 * 3^8.
%C A384791 Indices of records of the multiplicative function f(n) with f(p^e) = A008680(e).
%C A384791 All the terms are cubefull numbers since f(1) = 1 and f(n) = 0 if n is a noncubefull number.
%C A384791 The corresponding record values are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 20, ... (see the link for more values).
%C A384791 Every exponent must be the index of the first occurrence of A008680(e) in A008680. So possible exponents of prime factors of terms are 0, 8, 12, 15, 18, 20, ... - _David A. Corneth_, Jun 30 2025
%H A384791 David A. Corneth, <a href="/A384791/b384791.txt">Table of n, a(n) for n = 1..810</a> (first 216 terms from Amiram Eldar, terms <= 10^120)
%H A384791 David A. Corneth, <a href="/A384791/a384791.gp.txt">Table of n, a(n), exponents of prime factors and record values for n = 1..810</a>
%H A384791 <a href="/index/Pow#powerful">Index entries for sequences related to powerful numbers</a>.
%e A384791 256 in the sequence as 256 = 1^3 * 4^4 * 1^5 = 2^3 * 1^4 * 2^5 so there are two ways to write 256 as b^3 * c^4 * d^5, with b, c and d >= 1 and no smaller positive integer can be written in at least two ways like that. - _David A. Corneth_, Jun 30 2025
%t A384791 f[p_, e_] := Floor[(1+(-1)^e)*(-1)^Floor[e/2]/8 + (e^2 + 12*e + 90)/120]; 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 A384791 Subsequence of A025487, A036966 and A181800.
%Y A384791 Cf. A008680, A046055, A384789, A384790 (powerful analog).
%K A384791 nonn
%O A384791 1,2
%A A384791 _Amiram Eldar_, Jun 10 2025