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A003997
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Sums of distinct positive cubes.
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13
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1, 8, 9, 27, 28, 35, 36, 64, 65, 72, 73, 91, 92, 99, 100, 125, 126, 133, 134, 152, 153, 160, 161, 189, 190, 197, 198, 216, 217, 224, 225, 243, 244, 251, 252, 280, 281, 288, 289, 307, 308, 315, 316, 341, 342, 343, 344, 349, 350, 351, 352, 368, 369, 370, 371
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OFFSET
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1,2
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COMMENTS
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12758 is the largest of 2788 positive integers not in this sequence. - Jud McCranie, Dec 11 1999
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REFERENCES
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D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 12758.
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LINKS
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FORMULA
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MAPLE
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GF := series( (1+x)*(1+x^8)*(1+x^27)*(1+x^64)*(1+x^125)*(1+x^216)*(1+x^343)*(1+x^512)*(1+x^729)*(1+x^1000), x, 11^3); # Edited by M. F. Hasler, May 01 2020
A003997_upto := n -> map(degree, {op(convert(series(product(1 + x^(k^3), k = 1 .. floor(root(n, 3)))-1, x, n+1), `+`))}); # M. F. Hasler, May 01 2020;
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MATHEMATICA
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lim = 8; s = {0}; Do[s = Union[s, s + n^3], {n, lim}]; Select[s, 0 < # <= lim^3 &] (* T. D. Noe, Jul 10 2012 *)
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PROG
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(PARI) list(lim)={
lim\=1;
my(lm=min(lim+1, 12758), v=List(), P);
P=prod(n=1, lm^(1/3), 1+x^(n^3), 1+O(x^lm));
for(n=1, lm-1, if(polcoeff(P, n), listput(v, n)));
if(lim>12758, concat(Vec(v), vector(lim-12758, i, i+12758)), Vec(v))
(PARI) select( is_A003997(n, m=n)={m^3>n&&m=sqrtnint(n, 3); n==m^3||while(m>1, is_A003997(n-m^3, m--)&&return(1))}, [1..400]) \\ M. F. Hasler, Apr 21 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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