cp's OEIS Frontend

A334151 Numbers k such that k / rad(k) > m / rad(m) for all m < k.

%I A334151 #13 Mar 13 2023 06:06:20
%S A334151 1,4,8,16,27,32,64,128,243,256,512,1024,2048,4096,6561,8192,16384,
%T A334151 32768,59049,65536,131072,262144,524288,1048576,1594323,2097152,
%U A334151 4194304,8388608,14348907,16777216,33554432,67108864,129140163,134217728,268435456
%N A334151 Numbers k such that k / rad(k) > m / rad(m) for all m < k.
%C A334151 The terms listed in the Data section are numbers of the form 2^i or 3^ceiling(j*(1 + sqrt(2))), i >= 2, j >= 0 (empirical observation).
%H A334151 Michael De Vlieger, <a href="/A334151/b334151.txt">Table of n, a(n) for n = 1..4190</a>
%H A334151 Michael De Vlieger, <a href="/A334151/a334151.png">256 X 256 pixel bitmap</a> showing black if 3 | a(n) else white for n = 1..2^16, read in rows from left to right, stacked top to bottom.
%t A334151 pp = 4; nn = 2^29; j = 0; c = e[_] = 1; r = Prime@ Range[pp];
%t A334151 Do[(e[#1]++; Set[{k, m}, {#1^#2, #1^(#2 - 1)}]) & @@
%t A334151   First@ MinimalBy[Array[{#, e[#]} &[r[[#]]] &, pp], Power @@ # &];
%t A334151  If[m > j, Set[{a[c], j}, {k, m}]; c++];
%t A334151  If[k > nn/2, Break[]], {n, Infinity}];
%t A334151 {1}~Join~Array[a, c - 2, 2] (* _Michael De Vlieger_, Mar 11 2023 *)
%Y A334151 Cf. A003557, A006899, A007947, A064549.
%K A334151 nonn
%O A334151 1,2
%A A334151 _Ilya Gutkovskiy_, Apr 16 2020