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A003331
Numbers that are the sum of 8 positive cubes.
37
8, 15, 22, 29, 34, 36, 41, 43, 48, 50, 55, 57, 60, 62, 64, 67, 69, 71, 74, 76, 78, 81, 83, 85, 86, 88, 92, 93, 95, 97, 99, 100, 102, 104, 106, 107, 111, 112, 113, 114, 118, 119, 120, 121, 123, 125, 126, 130, 132, 133, 134, 137, 138, 139, 140, 141, 144, 145, 146, 148, 149
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
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
A003331(n)=if(n>478, n+142, n>329, n+141, A003331_upto(470)[n]) \\ M. F. Hasler, Aug 13 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:
A000404 (x=2, y=2), A000408 (3, 2), A000414 (4, 2), A047700 (5, 2),
A003325 (2, 3), A003072 (3, 3), A003327 .. A003335 (4 .. 12, 3),
A003336 .. A003346 (2 .. 12, 4), A003347 .. A003357 (2 .. 12, 5),
A003358 .. A003368 (2 .. 12, 6), A003369 .. A003379 (2 .. 12, 7),
A003380 .. A003390 (2 .. 12, 8), A003391 .. A004801 (2 .. 12, 9),
A004802 .. A004812 (2 .. 12, 10), A004813 .. A004823 (2 .. 12, 11).
Sequence in context: A070043 A003786 A008686 * A345783 A016993 A079043
KEYWORD
nonn,easy
STATUS
approved