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A154333 Difference between n^3 and the next smaller square.

%I A154333 #15 Jul 22 2025 06:18:04
%S A154333 1,4,2,15,4,20,19,28,53,39,35,47,81,40,11,127,13,56,135,79,45,39,67,
%T A154333 135,249,152,83,48,53,104,207,7,216,100,26,431,28,116,270,496,277,104,
%U A154333 546,503,524,615,139,368,685,391,155,732,652,648,726,55,293,631,170,704,405
%N A154333 Difference between n^3 and the next smaller square.
%C A154333 The sequence A077116(n) = n^3-[sqrt(n^3)]^2 satisfies A077116(n)=0 <=> n^3 is a square <=> n is a square. It differs from the present sequence (which is always positive) only in these indices, where a(k^2)=2k^3-1.
%H A154333 Harvey P. Dale, <a href="/A154333/b154333.txt">Table of n, a(n) for n = 1..1000</a>
%F A154333 a(n) = n^3 - [sqrt(n^3 - 1)]^2 = A000578(n) - A048760(n^3-1). a(k^2) = 2 k^3 - 1.
%F A154333 a(n) = A071797(n^3). - _R. J. Mathar_, May 29 2016
%p A154333 A154333 := proc(n)
%p A154333     A071797(n^3) ;
%p A154333 end proc: # _R. J. Mathar_, May 29 2016
%t A154333 nss[n_]:=Module[{n3=n^3,s},s=Floor[Sqrt[n3]]^2;If[s==n3,s=(Sqrt[s]- 1)^2, s]]; Table[n^3-nss[n],{n,70}] (* _Harvey P. Dale_, Jan 19 2017 *)
%o A154333 (PARI) A154333(n) = n^3-sqrtint(n^3-1)^2
%o A154333 a154333 = vector(90,n,n^3-sqrtint(n^3-1)^2)
%Y A154333 Cf. A087285 (range of this sequence, excluding the initial term 1).
%K A154333 nonn
%O A154333 1,2
%A A154333 _M. F. Hasler_, Jan 07 2009