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

%I A000093 M1344 N0515 #43 Jul 02 2025 16:01:53
%S A000093 0,1,2,5,8,11,14,18,22,27,31,36,41,46,52,58,64,70,76,82,89,96,103,110,
%T A000093 117,125,132,140,148,156,164,172,181,189,198,207,216,225,234,243,252,
%U A000093 262,272,281,291,301,311,322,332,343,353,364,374,385,396,407,419,430
%N A000093 a(n) = floor(n^(3/2)).
%D A000093 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.
%D A000093 N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D A000093 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A000093 Christian G. Bower, <a href="/A000093/b000093.txt">Table of n, a(n) for n=0..500</a>
%H A000093 B. K. Agarwala and F. C. Auluck, <a href="/A000093/a000093.pdf">Statistical mechanics and partitions into non-integral powers of integers</a>, Proc. Camb. Phil. Soc., 47 (1951), 207-216. [Annotated scanned copy]
%F A000093 a(n) = A077121(n) - 1. [_Reinhard Zumkeller_, Oct 31 2009]
%F A000093 a(n) = floor(n*sqrt(n)). [_Arkadiusz Wesolowski_, Jun 01 2011]
%F A000093 a(n) = A000196(A000578(n)) = A074704(n)+n*A000196(n). [_Reinhard Zumkeller_, Jun 27 2011]
%p A000093 Digits := 100: A000093 := n->floor(evalf(n^(3/2)));
%t A000093 Table[ Floor[ Sqrt[n^3]], {n, 0, 60}]
%o A000093 (PARI) a(n)=if(n<0,0,sqrtint(n^3))
%o A000093 (Haskell)
%o A000093 a000093 = a000196 . a000578  -- _Reinhard Zumkeller_, Jul 11 2014
%o A000093 (Python)
%o A000093 from math import isqrt
%o A000093 def A000093(n): return isqrt(n**3) # _Chai Wah Wu_, Sep 08 2024
%Y A000093 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).
%Y A000093 Cf. A002821.
%Y A000093 Cf. A185549.
%K A000093 nonn,easy
%O A000093 0,3
%A A000093 _N. J. A. Sloane_
%E A000093 More terms from _James Sellers_, May 04 2000