A079645 Numbers j such that the integer part of the cube root of j divides j.

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

Offset

1,2

Comments

Concrete Mathematics Casino Problem - Winners.

References

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. 2nd Edition. Addison-Wesley, Reading, MA, 1994. Section 3.2, pp. 74-76.

Links

G. C. Greubel, Table of n, a(n) for n = 1..10000

B. Cloitre, Some divisibility sequences.

Formula

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

Example

252^(1/3) = 6.316359597656... and 252/6 = 42 hence 252 is in the sequence.

Maple

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

Mathematica

Select[Range[1000], Mod[#, Floor[Power[#, 1/3]]] == 0 &]
Select[Range[1000], Divisible[#, Floor[CubeRoot[#]]]&] (* Harvey P. Dale, Jun 19 2023 *)

Prog

(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

Crossrefs

Cf. A006446, A032378, A079631, A112873, A120721.

Sequence in context: A018676 A115845 A026507 * A316114 A316115 A032958

Adjacent sequences: A079642 A079643 A079644 * A079646 A079647 A079648

Keyword

nonn

Author

Benoit Cloitre, Jan 31 2003

Status

approved