A353875 a(n) is the minimal n-digit number which can be the length of a side of a Pythagorean triangle in the largest number of ways.

5, 60, 840, 9240, 65520, 720720, 8168160, 98017920, 931170240, 9311702400, 80313433200, 931635825120, 9626903526240, 95492672074800, 890488576177200, 9973472053184640, 87624075895836480, 876240758958364800, 9419588158802421600, 99847634483305668960

Offset: 1

Author

Zhining Yang, Jun 26 2022

Keywords

• nonn
• base

Examples

			a(2)=60 because 60 is the minimal 2-digit number which can be the length of a side of an integer-sided right triangle in 14 distinct ways, (11, 60, 61), (25, 60, 65), (32, 60, 68), (36, 48, 60), (45, 60, 75), (60, 63, 87), (60, 80, 100), (60, 91, 109), (60, 144, 156), (60, 175, 185), (60, 221, 229), (60, 297, 303), (60, 448, 452), (60, 899, 901), and 14 is the maximum number of such ways for a 2-digit number.
		

Crossrefs

Cf. A046079, A046080.

Programs

Python

from sympy import factorint
def s(n):
    f=factorint(n)
    d, q=(list(f.keys()), list(f.values()))
    (a, b, c, x)=(0, 1, 1, 0)
    if(d[0]==2):
        a, x=(0, 1)
        if q[0]>1:
             a=q[0]-1
    for p in range(x, len(d)):
        b*=(1+2*q[p])
        if d[p]%4==1:
            c*=(1+2*q[p])
    return((b-1)//2+a*b+(c-1)//2)
def a(n):
    max=0
    for i in range(1+10**(n-1), 10**n):
        if s(i)>max:
            k,max=(i,s(i))
    return(n,[k,max])
for i in range(1,6):
    print (a(i))