cp's OEIS Frontend

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.

%I A115879 #14 Aug 21 2025 21:36:55
%S A115879 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,
%T A115879 18,48,210,8,240,12,22,144,6,24,342,180,26,15,420,20,462,120,12,264,
%U A115879 552,7,84,60,34,168,702,36,24,21,38,420,870,16,930,480,8,24,36,44
%N 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.
%H A115879 Robert Israel, <a href="/A115879/b115879.txt">Table of n, a(n) for n = 1..10000</a>
%e A115879 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).
%p A115879 f:= proc(n) local q;
%p A115879   q:= max(select(t -> t^2 < n^2 and n^2/t - t mod 4 = 0, numtheory:-divisors(n^2)));
%p A115879   if q = -infinity then 0 else (n^2/q - q)/4 fi;
%p A115879 end proc:
%p A115879 map(f, [$1..100]); # _Robert Israel_, Aug 21 2025
%o A115879 (Python)
%o A115879 from itertools import takewhile
%o A115879 from collections import deque
%o A115879 from sympy import divisors
%o A115879 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
%Y A115879 Cf. A067721, A115878, A115880, A115881.
%K A115879 nonn,look
%O A115879 1,3
%A A115879 _Giovanni Resta_, Feb 02 2006