Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #27 Jun 24 2024 23:28:53
%S 1,1,1,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,
%T 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,1,1,0,0,
%U 0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1
%N Number of partitions of n into 2 nonnegative cubes.
%C a(1729) = 2, the first point where a value larger than 1 appears, and where this sequence differs from A373972. - _Antti Karttunen_, Jun 24 2024
%H Antti Karttunen, <a href="/A025446/b025446.txt">Table of n, a(n) for n = 0..100080</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/1729_(number)">1729 (number)</a>
%F a(n) = A010057(n) + A025455(n) = A010057(n) XOR A025455(n). [The latter by Fermat's Last Theorem] - _Antti Karttunen_, Jun 24 2024
%e From _Antti Karttunen_, Jun 24 2024: (Start)
%e 8 = 0^3 + 2^3, and as there are no other partitions of 8 into 2 nonnegative cubes, a(8) = 1.
%e 16 = 2^3 + 2^3, and as there are no other partitions of 16 into 2 nonnegative cubes, a(16) = 1.
%e 1729 = 1^3 + 12^3 = 9^3 + 10^3, and as there are no other partitions of 1729 into 2 nonnegative cubes, a(1729) = 2.
%e (End)
%o (PARI) A025446(n) = if(n<=2, 1, my(s=0, x=sqrtnint(n,3)); forstep(i=x, 0, -1, my(x3=i^3, y3=n-x3); if(y3>x3, return(s), s += ispower(y3, 3)))); \\ _Antti Karttunen_, Jun 24 2024
%Y Cf. A010057, A025455, A004999 (indices of nonzero terms), A373972 (their characteristic function).
%K nonn
%O 0,1730
%A _David W. Wilson_
%E Data section extended up to a(126) and the secondary offset added by _Antti Karttunen_, Jun 24 2024