A047702 Numbers that are the sum of 3 but no fewer positive cubes.

3, 10, 17, 24, 29, 36, 43, 55, 62, 66, 73, 80, 81, 92, 99, 118, 127, 129, 134, 136, 141, 153, 155, 160, 179, 190, 192, 197, 218, 225, 232, 244, 251, 253, 258, 270, 277, 281, 288, 307, 314, 342, 345, 349, 352, 359, 368, 371, 375, 378, 397, 405, 408, 415, 433

Offset: 1

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn
• nice
• easy

Examples

			344 is in A003072, but also in A003325; therefore it is not in here.
		

References

• C. G. J. Jacobi, Gesammelte Werke, vol. 6, 1969, Chelsea, NY, p. 352.

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• C. G. J. Jacobi, Gesammelte Werke.
• Index entries for sequences related to sums of cubes

Crossrefs

Cf. A000419, A002376, A003072.

Programs

Maple

N:= 1000: # to get all terms <= N
G3:= series(add(x^(i^3),i=1..floor(N^(1/3)))^3,x,N+1):
G2:= series(add(x^(i^3),i=0..floor(N^(1/3)))^2,x,N+1):
select(t -> coeff(G3,x,t) > 0 and coeff(G2,x,t) = 0, [$1..N]); # Robert Israel, Dec 12 2016

Mathematica

Select[Range[500], (pr = PowersRepresentations[#, 3, 3]; pr != {} && Count[pr, r_ /; (Times @@ r) == 0] == 0) &][[1 ;; 55]]  (* Jean-François Alcover, Apr 08 2011 *)

Formula

The numbers in {A003072 MINUS A000578} MINUS A003325. - R. J. Mathar, Apr 13 2008