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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.
0
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
EXAMPLE
a(1) = 3 as 3 = 1 + 1 + 1 and 1 * 1 * 1 = 1 is a perfect cube.
MAPLE
N:= 2*10^4: m:= 67:
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 m from ceil((y/(b*c^2))^(1/3)) do
s:= x+y+m^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:
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:
convert(V, list); # Robert Israel, Oct 21 2024
CROSSREFS
Cf. A375580.
Sequence in context: A212995 A081849 A333667 * A169642 A222482 A022129
KEYWORD
nonn
AUTHOR
David A. Corneth, Aug 21 2024
STATUS
approved