A032378 Noncubes k that are divisible by floor(k^(1/3)).

2, 3, 4, 5, 6, 7, 10, 12, 14, 16, 18, 20, 22, 24, 26, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 68, 72, 76, 80, 84, 88, 92, 96, 100, 104, 108, 112, 116, 120, 124, 130, 135, 140, 145, 150, 155, 160, 165, 170, 175, 180, 185, 190, 195, 200, 205, 210, 215, 222, 228, 234, 240

Offset: 1

Author

N. J. A. Sloane, Dec 22 2001, corrected Oct 29 2006

Keywords

• nonn

Comments

The Concrete Math Club Casino problem - non-cube winning slots.

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

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A066353, A079645, A112873.

Programs

Magma

[k*j: j in [(k^2+1)..(k^2+3*k+3)], k in [1..6]]; // G. C. Greubel, Jul 20 2023

Maple

t1:=[]; for n from 1 to 500 do t2:=floor(n^(1/3)); if n mod t2 = 0 and t2^3 <> n then t1:=[op(t1),n]; fi; od:
# Alternate:
seq(seq(n,n=k^3+k..(k+1)^3-1,k),k=1..6); # Robert Israel, Mar 24 2020

Mathematica

Select[Range[300],!IntegerQ[Surd[#,3]]&&Divisible[#,Floor[Surd[#,3]]]&] (* Harvey P. Dale, May 13 2020 *)

Python

from itertools import count, islice
from sympy import integer_nthroot
def A032378_gen(): # generator of terms
    return filter(lambda x: not x%integer_nthroot(x,3)[0],(n+(k:=integer_nthroot(n, 3)[0])+int(n>=(k+1)**3-k) for n in count(1)))
A032378_list = list(islice(A032378_gen(),40)) # Chai Wah Wu, Oct 12 2024

SageMath

flatten([[k*j for j in range((k^2+1),(k^2+3*k+3)+1)] for k in range(1,7)]) # G. C. Greubel, Jul 20 2023