OFFSET
1,1
COMMENTS
620 is the largest among only 142 positive integers not in this sequence. This can be proved by induction. - M. F. Hasler, Aug 13 2020
LINKS
David A. Corneth, Table of n, a(n) for n = 1..10000
FORMULA
a(n) = 142 + n for all n > 478. - M. F. Hasler, Aug 13 2020
EXAMPLE
From David A. Corneth, Aug 01 2020: (Start)
1796 is in the sequence as 1796 = 4^3 + 4^3 + 4^3 + 4^3 + 5^3 + 7^3 + 7^3 + 9^3.
2246 is in the sequence as 2246 = 2^3 + 4^3 + 5^3 + 5^3 + 5^3 + 5^3 + 7^3 + 11^3.
3164 is in the sequence as 3164 = 5^3 + 5^3 + 6^3 + 6^3 + 8^3 + 8^3 + 9^3 + 9^3.(End)
MATHEMATICA
Module[{upto=200, c}, c=Floor[Surd[upto, 3]]; Select[Union[Total/@ Tuples[ Range[ c]^3, 8]], #<=upto&]] (* Harvey P. Dale, Jan 11 2016 *)
PROG
(PARI) (A003331_upto(N, k=8, m=3)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(150) \\ M. F. Hasler, Aug 02 2020
(Python)
from itertools import combinations_with_replacement as mc
def aupto(lim):
cbs = (i**3 for i in range(1, int((lim-7)**(1/3))+2))
return sorted(set(k for k in (sum(c) for c in mc(cbs, 8)) if k <= lim))
print(aupto(150)) # Michael S. Branicky, Aug 15 2021
CROSSREFS
Other sequences of numbers that are the sum of x nonzero y-th powers:
KEYWORD
nonn,easy
AUTHOR
STATUS
approved