A375618 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.

1, 3, 20, 21, 57, 94, 133, 219, 217, 273, 453, 434, 551, 589, 399, 791, 665, 893, 1321, 779, 1330, 1387, 1519, 1749, 1786, 2033, 1767, 2527, 2793, 1995, 4066, 3325, 4389, 5548, 4557, 3895, 4123, 5187, 5890, 5529, 5453, 8075, 6213, 7980, 7581, 7790, 11275, 8113, 11324, 9310

Offset

0,2

Links

David A. Corneth, Table of n, a(n) for n = 0..303

David A. Corneth, PARI program

Example

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

Maple

N:= 2*10^4:
V:= Array(1..N): count:= 0:
for x from 1 to N/3 do
  for y from x to (N-x)/2 do
     F:= ifactors(x*y)[2];
     b:= mul(t[1], t = select(s -> s[2] mod 3 = 2, F));
     c:= mul(t[1], t = select(s -> s[2] mod 3 = 1, F));
     for k from ceil((y/(b*c^2))^(1/3)) do
       s:= x+y+k^3 * b * c^2;
       if s > N then break fi;
       if s < x + 2*y then next fi;
       V[s]:= V[s]+1
od od od:
m:= max(V):
A:= Array(0..m): A[0]:= 1: count:= 1:
for i from 1 to N while count < m+1 do
  v:= V[i];
  if A[v] = 0 then A[v]:= i; count:= count+1 fi
od:
AL:= convert(V, list);
if not member(0, AL, 'r') then r:= m+2 fi;
AL[1..r-1]; # Robert Israel,  Oct 21 2024, corrected Aug 22 2025

Prog

(PARI) \\ See Corneth link

Crossrefs

Cf. A375580.

Sequence in context: A081849 A333667 A396020 * A169642 A222482 A022129

Adjacent sequences: A375615 A375616 A375617 * A375619 A375620 A375621

Keyword

nonn

Author

David A. Corneth, Aug 21 2024

Status

approved