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%I #42 Feb 01 2021 19:22:11
%S 1,4,8,9,16,25,27,32,36,48,49,54,64,72,81,100,108,121,125,128,144,162,
%T 169,192,196,200,216,225,243,250,256,288,289,324,343,361,375,384,392,
%U 400,405,432,441,484,486,500,512,529,567,576,625,640,648,675,676,686,729,768
%N Numbers k such that (k*i)^(1/4) is an integer for some i in 1 <= i <= k.
%H Robert Israel, <a href="/A339497/b339497.txt">Table of n, a(n) for n = 1..10000</a>
%e 9 is in the sequence since (9*9)^(1/4) = 3 (an integer), with 1 <= 9 <= 9.
%p filter:= proc(n) local F,x,t;
%p F:= ifactors(n)[2];
%p x:= mul(t[1]^(-t[2] mod 4),t=F);
%p x <= n
%p end proc:
%p select(filter, [$1..1000]); # _Robert Israel_, Dec 29 2020
%t Table[If[Sum[1 - Ceiling[(n*k)^(1/4)] + Floor[(n*k)^(1/4)], {k, n}] > 0, n, {}], {n, 500}] // Flatten
%Y Cf. A339462.
%K nonn
%O 1,2
%A _Wesley Ivan Hurt_, Dec 27 2020
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