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

1, 4, 2, 15, 4, 20, 19, 28, 53, 39, 35, 47, 81, 40, 11, 127, 13, 56, 135, 79, 45, 39, 67, 135, 249, 152, 83, 48, 53, 104, 207, 7, 216, 100, 26, 431, 28, 116, 270, 496, 277, 104, 546, 503, 524, 615, 139, 368, 685, 391, 155, 732, 652, 648, 726, 55, 293, 631, 170, 704, 405

Offset: 1

Author

M. F. Hasler, Jan 07 2009

Keywords

• nonn

Comments

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.

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Maple

A154333 := proc(n)
    A071797(n^3) ;
end proc: # R. J. Mathar, May 29 2016

Mathematica

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 *)

PARI

A154333(n) = n^3-sqrtint(n^3-1)^2
a154333 = vector(90,n,n^3-sqrtint(n^3-1)^2)

Formula

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

a(n) = A071797(n^3). - R. J. Mathar, May 29 2016