A000093 a(n) = floor(n^(3/2)). (Formerly M1344 N0515)

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

0,3

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]

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]

Maple

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

Mathematica

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

Prog

(PARI) a(n)=if(n<0, 0, sqrtint(n^3))
(Haskell)
a000093 = a000196 . a000578  -- Reinhard Zumkeller, Jul 11 2014
(Python)
from math import isqrt
def A000093(n): return isqrt(n**3) # Chai Wah Wu, Sep 08 2024

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.

Sequence in context: A192585 A344162 A163516 * A324476 A070214 A330031

Adjacent sequences: A000090 A000091 A000092 * A000094 A000095 A000096

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

More terms from James A. Sellers, May 04 2000

Status

approved