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

1,2

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

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A360084 A019061 A019012 * A185130 A261870 A325516

Adjacent sequences: A154330 A154331 A154332 * A154334 A154335 A154336

Keyword

nonn

Author

M. F. Hasler, Jan 07 2009

Status

approved