A397778 Lengths of longest legs of Pythagorean triangles corresponding to a record number of such triangles.

4, 12, 24, 60, 120, 240, 360, 720, 840, 1680, 2520, 3360, 5040, 9240, 15120, 18480, 27720, 36960, 55440, 110880, 166320, 221760, 240240, 360360, 480480, 720720, 1441440, 2162160, 2882880, 3603600, 4084080, 4324320, 6126120, 8168160, 12252240, 24504480, 36756720, 49008960, 61261200, 73513440, 98017920

Offset

1,1

Comments

Indices of record values in A056137.

Links

Table of n, a(n) for n=1..41.

Example

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.

Prog

(PARI) \\ b(n) is A056137(n)
b(n) = my(r=n^2); sumdiv(r, d, my(t=r/d-d); t>0 && t%2 == 0 && t^2<4*r)
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

Crossrefs

Cf. A056137.

Sequence in context: A394935 A356550 A216244 * A215223 A318610 A296358

Adjacent sequences: A397775 A397776 A397777 * A397787 A397788 A397790

Keyword

nonn,new

Author

Richard R. Forberg, Jul 09 2026

Extensions

a(31)-a(33) corrected and more terms added by Andrew Howroyd, Jul 11 2026

Status

approved