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A339497 Numbers k such that (k*i)^(1/4) is an integer for some i in 1 <= i <= k. 2

%I

%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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Last modified June 19 12:02 EDT 2021. Contains 345128 sequences. (Running on oeis4.)