A154333 - OEIS

%I #13 Jan 19 2017 09:34:12

%S 1,4,2,15,4,20,19,28,53,39,35,47,81,40,11,127,13,56,135,79,45,39,67,

%T 135,249,152,83,48,53,104,207,7,216,100,26,431,28,116,270,496,277,104,

%U 546,503,524,615,139,368,685,391,155,732,652,648,726,55,293,631,170,704,405

%N Difference between n^3 and the next smaller square

%C 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 Harvey P. Dale, <a href="/A154333/b154333.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = n^3 - [sqrt(n^3 - 1)]^2 = A000578(n) - A048760(n^3-1). a(k^2) = 2 k^3 - 1.

%F a(n) = A071797(n^3). - _R. J. Mathar_, May 29 2016

%p A154333 := proc(n)

%p     A071797(n^3) ;

%p end proc: # _R. J. Mathar_, May 29 2016

%t 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 (PARI) A154333(n) = n^3-sqrtint(n^3-1)^2

%o a154333 = vector(90,n,n^3-sqrtint(n^3-1)^2)

%Y Cf. A087285 (range of this sequence, excluding the initial term 1).

%K nonn

%O 1,2

%A _M. F. Hasler_, Jan 07 2009