

A154333


Difference between n^3 and the next smaller square


6



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
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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^31.


LINKS



FORMULA

a(n) = n^3  [sqrt(n^3  1)]^2 = A000578(n)  A048760(n^31). a(k^2) = 2 k^3  1.


MAPLE



MATHEMATICA

nss[n_]:=Module[{n3=n^3, s}, s=Floor[Sqrt[n3]]^2; If[s==n3, s=(Sqrt[s] 1)^2, s]]; Table[n^3nss[n], {n, 70}] (* Harvey P. Dale, Jan 19 2017 *)


PROG

(PARI) A154333(n) = n^3sqrtint(n^31)^2
a154333 = vector(90, n, n^3sqrtint(n^31)^2)


CROSSREFS

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


KEYWORD

nonn


AUTHOR



STATUS

approved



