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A295976 Number of nonnegative solutions to (x,y) = 1 and x^3 + y^3 = n.

%I A295976 #16 May 31 2021 17:46:22
%S A295976 0,2,1,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,
%T A295976 0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,
%U A295976 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2
%N A295976 Number of nonnegative solutions to (x,y) = 1 and x^3 + y^3 = n.
%C A295976 Number of ordered pairs of two nonnegative natural numbers that are coprime and whose cubes add to n. - _Antti Karttunen_, May 31 2021
%H A295976 Antti Karttunen, <a href="/A295976/b295976.txt">Table of n, a(n) for n = 0..65537</a>
%e A295976 For 1729, a(1729) = 4, because the following four ordered pairs, (1,12),  (9,10),  (10,9) and (12,1) satisfy the condition, as 1^3 + 12^3 = 9^3 + 10^3 = 1729. - _Antti Karttunen_, May 31 2021
%o A295976 (PARI) {a(n) = sum(i=0, n, sum(j=0, n, if((gcd(i, j)==1) && (i^3+j^3==n), 1, 0)))}
%o A295976 (PARI) A295976(n) = { my(s=0); for(i=0, oo, i3 = i^3; forstep(j=n-i3, 0, -1, if((i3+j^3==n) && gcd(i, j)==1, s++)); if(i3>n, return(s))); }; \\ _Antti Karttunen_, May 31 2021
%Y A295976 Cf. A173677, A225530, A295819, A295977.
%Y A295976 Cf. also A202679.
%K A295976 nonn
%O A295976 0,2
%A A295976 _Seiichi Manyama_, Dec 01 2017