A115879 a(n) is the least positive x satisfying the Diophantine equation x^2=y(y+n). a(n)=0 if there are no solutions.

0, 0, 2, 0, 6, 4, 12, 3, 6, 12, 30, 8, 42, 24, 4, 6, 72, 12, 90, 24, 10, 60, 132, 5, 30, 84, 18, 48, 210, 8, 240, 12, 22, 144, 6, 24, 342, 180, 26, 15, 420, 20, 462, 120, 12, 264, 552, 7, 84, 60, 34, 168, 702, 36, 24, 21, 38, 420, 870, 16, 930, 480, 8, 24, 36, 44

Offset: 1

Author

Giovanni Resta, Feb 02 2006

Keywords

• nonn
• look

Examples

			a(15)=4 since the solutions (x,y) to x^2=y(y+15) are (4,1), (10,5), (18, 12) and (56, 49). The least x values is 4, from (x,y)=(4,1).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A067721, A115878, A115880, A115881.

Programs

Maple

f:= proc(n) local q;
  q:= max(select(t -> t^2 < n^2 and n^2/t - t mod 4 = 0, numtheory:-divisors(n^2)));
  if q = -infinity then 0 else (n^2/q - q)/4 fi;
end proc:
map(f, [$1..100]); # Robert Israel, Aug 21 2025

Python

from itertools import takewhile
from collections import deque
from sympy import divisors
def A115879(n): return -(a:=next(iter(deque((d for d in takewhile(lambda d:d>2 # Chai Wah Wu, Aug 21 2024