OFFSET
1,1
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
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 *)
PROG
(Magma) [k*j: j in [(k^2+1)..(k^2+3*k+3)], k in [1..6]]; // G. C. Greubel, Jul 20 2023
(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
(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)))
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 22 2001, corrected Oct 29 2006
STATUS
approved