cp's OEIS Frontend

A089058 Each positive number x is repeated m times, where there are m numbers y >= x such that x*y/(x+y) is an integer.

%I A089058 #12 May 30 2025 01:12:21
%S A089058 2,3,4,4,5,6,6,6,7,8,8,8,9,9,10,10,10,10,11,12,12,12,12,12,13,14,14,
%T A089058 14,14,15,15,15,16,16,16,16,17,18,18,18,18,18,18,19,20,20,20,20,20,20,
%U A089058 21,21,21,21,22,22,22,22
%N A089058 Each positive number x is repeated m times, where there are m numbers y >= x such that x*y/(x+y) is an integer.
%C A089058 xy/(x+y) is the side of the inscribed square of a right triangle with integer legs x and y.
%C A089058 The number of repetitions of x is the number of divisors of x^2 that are at most x/2. - _Robert Israel_, May 25 2025
%H A089058 Robert Israel, <a href="/A089058/b089058.txt">Table of n, a(n) for n = 1..10010</a>
%e A089058 For x = 6 there are 3 possible y, namely 6, 12 and 30, with 6*6/(6+6) = 3, 6*12/(6+12) = 4 and 6*30/(6+30) = 5, so 6 occurs 3 times in the sequence. - _Robert Israel_, May 28 2025
%p A089058 f:= n -> nops(select(`<=`, numtheory:-divisors(n^2),n/2)):
%p A089058 seq(n$f(n), n=1..30)]; # _Robert Israel_, May 25 2025
%o A089058 (PARI) xydivxpy(n) = { for(x=1,n, for(y=x,n, h=x*y/(x+y); if(h==floor(h), print1(x","); ) ) ) }
%K A089058 nonn
%O A089058 1,1
%A A089058 _Cino Hilliard_, Dec 02 2003, corrected Nov 23 2006
%E A089058 Definition corrected by _Robert Israel_, May 25 2025