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A254767 a(n) is the least k > n such that k*n is a cube.

%I A254767 #24 Nov 12 2024 22:17:26
%S A254767 8,4,9,16,25,36,49,27,24,100,121,18,169,196,225,32,289,96,361,50,441,
%T A254767 484,529,72,40,676,64,98,841,900,961,54,1089,1156,1225,48,1369,1444,
%U A254767 1521,200,1681,1764,1849,242,75,2116,2209,288,56,160,2601,338,2809,108
%N A254767 a(n) is the least k > n such that k*n is a cube.
%C A254767 a(n) <= n^2 for all n > 1 because n * n^2 = n^3.
%H A254767 Peter Kagey, <a href="/A254767/b254767.txt">Table of n, a(n) for n = 1..5000</a>
%e A254767 a(12) = 18 because 12*18 = 6^3 (and 12*13, 12*14, 12*15, 12*16, 12*17 are not perfect cubes).
%t A254767 f[n_] := Block[{k = n + 1}, While[! IntegerQ@ Power[k n, 1/3], k++]; k]; Array[f, 54] (* _Michael De Vlieger_, Mar 17 2015 *)
%o A254767 (Ruby)
%o A254767 def a(n)
%o A254767   min = (n**(2/3.0)).ceil
%o A254767   (min..n+1).each { |i| return i**3/n if i**3 % n == 0 && i**3 > n**2 }
%o A254767 end
%o A254767 (PARI) a(n)=if (n==1, 8, for(k=n+1, n^2, if(ispower(k*n, 3), return(k))))
%o A254767 vector(100, n, a(n)) \\ _Derek Orr_, Feb 07 2015
%o A254767 (PARI) a(n) = {f = factor(n); for (i=1, #f~, if (f[i,2] % 3, f[i,2] = 3 - f[i,2]);); cb = factorback(f); cbr = sqrtnint(cb*n, 3); cb = cbr^3; k = cb/n; while((type(k=cb/n) != "t_INT") || (k<=n), cbr++; cb = cbr^3;); k;} \\ _Michel Marcus_, Mar 14 2015
%Y A254767 Cf. A072905 (an analogous sequence for squares).
%Y A254767 Cf. A048798 (similar sequence, no restriction that a(n) > n).
%K A254767 nonn,easy
%O A254767 1,1
%A A254767 _Peter Kagey_, Feb 07 2015