A375618 - OEIS

%I #10 Oct 23 2024 00:40:52

%S 1,3,20,21,57,94,133,219,217,273,453,434,551,589,399,791,665,893,1321,

%T 779,1330,1387,1519,1749,1786,2033,1767,2527,2793,1995,4066,3325,4389,

%U 5548,4557,3895,4123,5187,5890,5529,5453,8075,6213,7980,7581,7790,11275,8113,11324,9310

%N a(n) is the least positive integer k such that there are n partitions k = x + y + z of positive integers such that x * y * z is a perfect cube or -1 if no such positive integer exists.

%e a(1) = 3 as 3 = 1 + 1 + 1 and 1 * 1 * 1 = 1 is a perfect cube.

%p N:= 2*10^4: m:= 67:

%p V:= Array(1..N): count:= 0:

%p for x from 1 to N/3 do

%p   for y from x to (N-x)/2 do

%p      F:= ifactors(x*y)[2];

%p      b:= mul(t[1],t = select(s -> s[2] mod 3 = 2, F));

%p      c:= mul(t[1],t = select(s -> s[2] mod 3 = 1, F));

%p      for m from ceil((y/(b*c^2))^(1/3)) do

%p        s:= x+y+m^3 * b * c^2;

%p        if s > N then break fi;

%p        if s < x + 2*y then next fi;

%p        V[s]:= V[s]+1

%p od od od:

%p A:= Array(0..m): A[0]:= 1: count:= 1:

%p for i from 1 to N while count < m+1 do

%p   v:= V[i];

%p   if A[v] = 0 then A[v]:= i; count:= count+1 fi

%p od:

%p convert(V,list); # _Robert Israel_, Oct 21 2024

%Y Cf. A375580.

%K nonn

%O 0,2

%A _David A. Corneth_, Aug 21 2024