A186147 Rank of n^3 when {i^2: i>=1} and {j^3: j>=1} are jointly ranked with i^2 after j^3 when i^2=j^3. Complement of A135674.

1, 4, 8, 11, 16, 20, 25, 30, 35, 41, 47, 53, 59, 66, 73, 79, 87, 94, 101, 109, 117, 125, 133, 141, 149, 158, 167, 176, 185, 194, 203, 213, 222, 232, 242, 251, 262, 272, 282, 292, 303, 314, 324, 335, 346, 357, 369, 380, 391, 403, 415, 426, 438, 450, 462, 475, 487, 499, 512, 524, 537, 550, 563, 575, 589, 602, 615, 628, 642, 655, 669, 682, 696, 710, 724, 738, 752, 766, 781, 795, 809, 824, 839, 853, 868, 883, 898, 913

Offset

1,2

Comments

See A186145.

Links

Table of n, a(n) for n=1..88.

Formula

b(n) = n + floor((n^3-1/2)^(1/2)), as in the Mathematica program.

a(n) = n + floor(n^(3/2)) - 1 if n is square and a(n) = n + floor(n^(3/2)) otherwise. - Chai Wah Wu, Oct 15 2025

Mathematica

d=-1/2;
a[n_]:=n+Floor[(n^2-d)^(1/3)]; (* rank of n^2 *)
b[n_]:=n+Floor[(n^3+d)^(1/2)]; (* rank of n^3-1/2 *)
Table[a[n], {n, 1, 100}]  (* A135674 *)
Table[b[n], {n, 1, 100}]  (* A186147 *)

Prog

(Python)
from math import isqrt
from sympy.ntheory.primetest import is_square
def A186147(n): return n+isqrt(n**3)-is_square(n) # Chai Wah Wu, Oct 15 2025

Crossrefs

Cf. A135674, A186145.

Sequence in context: A311061 A317331 A311062 * A311063 A311064 A311065

Adjacent sequences: A186144 A186145 A186146 * A186148 A186149 A186150

Keyword

nonn

Author

Clark Kimberling, Feb 13 2011

Status

approved