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A079645
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Numbers j such that the integer part of the cube root of j divides j.
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5
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1, 2, 3, 4, 5, 6, 7, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 64, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 125, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210
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OFFSET
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1,2
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COMMENTS
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Concrete Mathematics Casino Problem - Winners.
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REFERENCES
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R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994. Section 3.2, pp. 74-76.
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LINKS
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FORMULA
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For n = (k/2)*(3*k+11) - m for some fixed m >= 0 with n > ((k-1)/2)*(3*(k-1) + 11) we have a(n) = k^3 + 3*k^2 + (3-m)*k. - Benoit Cloitre, Jan 22 2012
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EXAMPLE
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252^(1/3) = 6.316359597656... and 252/6 = 42 hence 252 is in the sequence.
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MAPLE
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t1:=[]; for n from 1 to 500 do t2:=floor(n^(1/3)); if n mod t2 = 0 then t1:=[op(t1), n]; fi; od: t1; # N. J. A. Sloane, Oct 29 2006
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MATHEMATICA
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Select[Range[1000], Mod[#, Floor[Power[#, 1/3]]] == 0 &]
Select[Range[1000], Divisible[#, Floor[CubeRoot[#]]]&] (* Harvey P. Dale, Jun 19 2023 *)
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PROG
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(Magma) [n: n in [1..250] | n mod Floor(n^(1/3)) eq 0 ]; // G. C. Greubel, Jul 20 2023
(SageMath) [n for n in (1..250) if n%(floor(n^(1/3)))==0 ] # G. C. Greubel, Jul 20 2023
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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