A003997 Sums of distinct positive cubes.

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

Offset

1,2

Comments

12758 is the largest of 2788 positive integers not in this sequence. - Jud McCranie, Dec 11 1999

References

D. Wells, The Penguin Dictionary of Curious and Interesting Numbers, entry 12758.

Links

T. D. Noe, Table of n, a(n) for n = 1..10000

R. Sprague, Über Zerlegungen in n-te Potenzen mit lauter verschiedenen Grundzahlen, Math. Z. 51, (1948), 466-468.

Index entries for linear recurrences with constant coefficients, signature (2,-1).

Formula

For n > 9970, a(n) = n + 2788. - Charles R Greathouse IV, Sep 02 2011

Maple

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;

Mathematica

lim = 8; s = {0}; Do[s = Union[s, s + n^3], {n, lim}]; Select[s, 0 < # <= lim^3 &] (* T. D. Noe, Jul 10 2012 *)

Prog

(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))
}; \\ Charles R Greathouse IV, Sep 02 2011
(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

Crossrefs

Complement of A001476. Cf. A003995.

Sequence in context: A305336 A042311 A371629 * A114090 A351959 A217843

Adjacent sequences: A003994 A003995 A003996 * A003998 A003999 A004000

Keyword

nonn,easy

Author

N. J. A. Sloane

Extensions

Definition clarified by Jeppe Stig Nielsen, Jan 27 2015

Status

approved