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A154333
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Difference between n^3 and the next smaller square
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6
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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
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1,2
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COMMENTS
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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.
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LINKS
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Harvey P. Dale, Table of n, a(n) for n = 1..1000
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FORMULA
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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
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MAPLE
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A154333 := proc(n)
A071797(n^3) ;
end proc: # R. J. Mathar, May 29 2016
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MATHEMATICA
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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 *)
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PROG
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(PARI) A154333(n) = n^3-sqrtint(n^3-1)^2
a154333 = vector(90, n, n^3-sqrtint(n^3-1)^2)
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CROSSREFS
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Cf. A087285 (range of this sequence, excluding the initial term 1).
Sequence in context: A087957 A019061 A019012 * A185130 A261870 A299789
Adjacent sequences: A154330 A154331 A154332 * A154334 A154335 A154336
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KEYWORD
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nonn
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AUTHOR
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M. F. Hasler, Jan 07 2009
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STATUS
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approved
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