A277781 - OEIS

%I #17 Nov 25 2019 01:10:28

%S 8,4,9,16,25,36,49,27,24,80,88,18,104,112,120,32,136,96,152,50,168,

%T 176,184,72,40,208,64,98,232,240,248,54,264,272,280,48,296,304,312,

%U 135,328,336,344,242,75,368,376,162,56,160,408,338,424,108,440,189,456

%N a(n) is the least k > n such that n*k or n*k^2 is a cube.

%C a(n) is 1-to-1.

%H Charles R Greathouse IV, <a href="/A277781/b277781.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = min(A254767(n), A277780(n)).

%e a(2)  = 4  because 2  * 4    =  2^3;

%e a(10) = 80 because 10 * 80^2 = 40^3.

%t Table[SelectFirst[n + Range[7 + n^2], AnyTrue[Power[#, 1/3] & /@ {n #, n #^2}, IntegerQ] &], {n, 57}] (* _Michael De Vlieger_, Feb 03 2018 *)

%o (PARI) a(n)=my(f=factor(n),tf=f,a,b); tf[,2]%=3; b=factorback(tf); tf[,2]=2*f[,2]%3; a=factorback(tf); min((sqrtnint(n\a,3)+1)^3*a, (sqrtnint(n\b,3)+1)^3*b) \\ _Charles R Greathouse IV_, Oct 31 2016

%Y Cf. A072905, A254767, A277780.

%K nonn,look

%O 1,1

%A _Peter Kagey_, Oct 30 2016