A257853 a(n) = 2*n^3 - floor(2^(1/3)*n)^3.

0, 1, 8, 27, 3, 34, 89, 174, 24, 127, 272, 465, 81, 298, 575, 918, 192, 565, 1016, 1551, 375, 946, 1613, 2382, 648, 1459, 2384, 62, 1029, 2122, 3347, 263, 1536, 2953, 4520, 566, 2187, 3970, 5921, 989, 3000, 5191, 7568, 1550, 3993, 6634, 9479, 2267, 5184, 8317

Offset

0,3

Comments

Is there a simple expression for a nontrivial lower bound for a(n)?

Links

Table of n, a(n) for n=0..49.

Example

a(4) = 2*4^3 - floor(2^(1/3)*4)^3 = 2*64 - 5^3 = 3.
a(5) = 2*5^3 - floor(2^(1/3)*5)^3 = 2*125 - 6^3 = 34.

Mathematica

Table[2 n^3 - Floor[2^(1/3) n]^3, {n, 0, 60}] (* Vincenzo Librandi, May 29 2015

Prog

(PARI) f(n, e=3, b=2)=n^e*b-floor(sqrtn(b, e)*n)^e
(Magma) [2*n^3 - Floor(2^(1/3)*n)^3: n in [0..50]]; // Vincenzo Librandi, May 29 2015

Crossrefs

Cf. A087056 (analog for squares), A257854, A257855 (4th & 5th power).

Sequence in context: A334659 A350625 A070493 * A070492 A070711 A282462

Adjacent sequences: A257850 A257851 A257852 * A257854 A257855 A257856

Keyword

nonn,easy

Author

M. F. Hasler, May 28 2015

Status

approved