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

1,1

Links

Table of n, a(n) for n=1..20.

Example

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.

Prog

(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))

Crossrefs

Cf. A046079, A046080.

Sequence in context: A320361 A138134 A283779 * A370445 A093885 A192948

Adjacent sequences: A353872 A353873 A353874 * A353876 A353877 A353878

Keyword

nonn,base

Author

Zhining Yang, Jun 26 2022

Status

approved