A382838 a(n) is the least k such that there are exactly n solutions in positive integers to the equation x^3 + y^2 = k^2.

1, 3, 15, 105, 665, 1155, 9240, 68265, 200640, 54285, 434280, 3474240, 19120920, 1430715, 451605, 38629305, 3612840, 28902720, 97546680, 154900515, 451605000, 1239204120, 2633760360, 12193335000, 21070082880, 28902720000

Offset

0,2

Links

Table of n, a(n) for n=0..25.

Example

a(2) = 15 because 15^2 = 225 can be expressed in exactly 2 ways as x^3 + y^2 with x, y > 0, namely  5^3 + 10^2 = 6^3 + 3^2, and no smaller number works.

Maple

N:= 10^8:
V:= Vector(N, datatype=integer[1]):
for x from 1 to floor(N^(2/3)) do
  for b in sort(convert(numtheory:-divisors(x^3), list)) do
    a:= x^3/b;
    if b >= a then break fi;
    if (b-a)::even then
       k:= (a+b)/2;
       if k <= N and V[1] < 127 then V[k]:= V[k]+1 fi;
    fi
   od;
od:
W:= Array(0..17): count:= 0:
for i from 1 to N while count < 18 do
   if W[V[i]] = 0 then W[V[i]]:= i; count:= count+1 fi
od:
convert(W, list);

Crossrefs

Cf. A382338.

Sequence in context: A001801 A323551 A267840 * A067546 A015682 A291744

Adjacent sequences: A382835 A382836 A382837 * A382839 A382840 A382841

Keyword

nonn,more

Author

Robert Israel, Apr 06 2025

Extensions

a(19) from Giorgos Kalogeropoulos, Apr 10 2025

a(20)-a(25) from Bert Dobbelaere, Apr 12 2025

Status

approved