A000093 a(n) = floor(n^(3/2)).

0, 1, 2, 5, 8, 11, 14, 18, 22, 27, 31, 36, 41, 46, 52, 58, 64, 70, 76, 82, 89, 96, 103, 110, 117, 125, 132, 140, 148, 156, 164, 172, 181, 189, 198, 207, 216, 225, 234, 243, 252, 262, 272, 281, 291, 301, 311, 322, 332, 343, 353, 364, 374, 385, 396, 407, 419, 430

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

References

• B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216.
• N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Christian G. Bower, Table of n, a(n) for n=0..500
• B. K. Agarwala and F. C. Auluck, Statistical mechanics and partitions into non-integral powers of integers, Proc. Camb. Phil. Soc., 47 (1951), 207-216. [Annotated scanned copy]

Crossrefs

Integer part of square root of n^k: A000196 (k=1), this sequence (k=3), A155013 (k=5), A155014 (k=7), A155015 (k=11), A155016 (k=13), A155018 (k=15), A155019 (k=17).

Cf. A002821.

Cf. A185549.

Programs

Haskell

a000093 = a000196 . a000578  -- Reinhard Zumkeller, Jul 11 2014

Maple

Digits := 100: A000093 := n->floor(evalf(n^(3/2)));

Mathematica

Table[ Floor[ Sqrt[n^3]], {n, 0, 60}]

PARI

a(n)=if(n<0,0,sqrtint(n^3))

Python

from math import isqrt
def A000093(n): return isqrt(n**3) # Chai Wah Wu, Sep 08 2024

Formula

a(n) = A077121(n) - 1. [Reinhard Zumkeller, Oct 31 2009]

a(n) = floor(n*sqrt(n)). [Arkadiusz Wesolowski, Jun 01 2011]

a(n) = A000196(A000578(n)) = A074704(n)+n*A000196(n). [Reinhard Zumkeller, Jun 27 2011]

Extensions

More terms from James Sellers, May 04 2000