A277781 a(n) is the least k > n such that n*k or n*k^2 is a cube.

8, 4, 9, 16, 25, 36, 49, 27, 24, 80, 88, 18, 104, 112, 120, 32, 136, 96, 152, 50, 168, 176, 184, 72, 40, 208, 64, 98, 232, 240, 248, 54, 264, 272, 280, 48, 296, 304, 312, 135, 328, 336, 344, 242, 75, 368, 376, 162, 56, 160, 408, 338, 424, 108, 440, 189, 456

Offset

1,1

Comments

a(n) is 1-to-1.

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Formula

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

Example

a(2)  = 4  because 2  * 4    =  2^3;
a(10) = 80 because 10 * 80^2 = 40^3.

Mathematica

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

Prog

(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

Crossrefs

Cf. A072905, A254767, A277780.

Sequence in context: A011196 A205184 A105144 * A254767 A194184 A194217

Adjacent sequences: A277778 A277779 A277780 * A277782 A277783 A277784

Keyword

nonn,look

Author

Peter Kagey, Oct 30 2016

Status

approved