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

1,3

Links

Table of n, a(n) for n=1..66.

Example

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).

Prog

(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<n, divisors(n**2)) if not (d-n**2//d)&3), 1)), 0))+(n**2//a if a else 0)>>2 # Chai Wah Wu, Aug 21 2024

Crossrefs

Cf. A067721, A115878, A115880, A115881.

Sequence in context: A131595 A290826 A124228 * A115880 A335728 A078037

Adjacent sequences: A115876 A115877 A115878 * A115880 A115881 A115882

Keyword

nonn

Author

Giovanni Resta, Feb 02 2006

Status

approved