A397778 - OEIS

%I #23 Jul 20 2026 23:58:59

%S 4,12,24,60,120,240,360,720,840,1680,2520,3360,5040,9240,15120,18480,

%T 27720,36960,55440,110880,166320,221760,240240,360360,480480,720720,

%U 1441440,2162160,2882880,3603600,4084080,4324320,6126120,8168160,12252240,24504480,36756720,49008960,61261200,73513440,98017920

%N Lengths of longest legs of Pythagorean triangles corresponding to a record number of such triangles.

%C Indices of record values in A056137.

%e For a right triangle with longest leg of 60, the lengths other sides are: 11,25,32,45. The corresponding hypotenuses are: 61,65,68,75. All triangles with a longest leg of less than 60 have 3 or fewer triangles.

%o (PARI) \\ b(n) is A056137(n)

%o b(n) = my(r=n^2); sumdiv(r, d, my(t=r/d-d); t>0 && t%2 == 0 && t^2<4*r)

%o upto(lim) = { my(m=0,L=List()); for(i=1, lim, if(numdiv(i^2)>2*m, my(t=b(i));if(t>m,m=t; listput(L,i)))); Vec(L) } \\ _Andrew Howroyd_, Jul 10 2026

%Y Cf. A056137.

%K nonn,new

%O 1,1

%A _Richard R. Forberg_, Jul 09 2026

%E a(31)-a(33) corrected and more terms added by _Andrew Howroyd_, Jul 11 2026