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
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).
Programs
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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;
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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 *) -
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
Formula
For n > 9970, a(n) = n + 2788. - Charles R Greathouse IV, Sep 02 2011
Extensions
Definition clarified by Jeppe Stig Nielsen, Jan 27 2015
Comments