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

1, 4, 8, 16, 27, 32, 64, 128, 243, 256, 512, 1024, 2048, 4096, 6561, 8192, 16384, 32768, 59049, 65536, 131072, 262144, 524288, 1048576, 1594323, 2097152, 4194304, 8388608, 14348907, 16777216, 33554432, 67108864, 129140163, 134217728, 268435456

Offset: 1

Author

Ilya Gutkovskiy, Apr 16 2020

Keywords

• nonn

Comments

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).

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..4190
• Michael De Vlieger, 256 X 256 pixel bitmap showing black if 3 | a(n) else white for n = 1..2^16, read in rows from left to right, stacked top to bottom.

Crossrefs

Cf. A003557, A006899, A007947, A064549.

Programs

Mathematica

pp = 4; nn = 2^29; j = 0; c = e[_] = 1; r = Prime@ Range[pp];
Do[(e[#1]++; Set[{k, m}, {#1^#2, #1^(#2 - 1)}]) & @@
  First@ MinimalBy[Array[{#, e[#]} &[r[[#]]] &, pp], Power @@ # &];
 If[m > j, Set[{a[c], j}, {k, m}]; c++];
 If[k > nn/2, Break[]], {n, Infinity}];
{1}~Join~Array[a, c - 2, 2] (* Michael De Vlieger, Mar 11 2023 *)