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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.
1
5, 60, 840, 9240, 65520, 720720, 8168160, 98017920, 931170240, 9311702400, 80313433200, 931635825120, 9626903526240, 95492672074800, 890488576177200, 9973472053184640, 87624075895836480, 876240758958364800, 9419588158802421600, 99847634483305668960
OFFSET
1,1
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
Sequence in context: A320361 A138134 A283779 * A370445 A093885 A192948
KEYWORD
nonn,base
AUTHOR
Zhining Yang, Jun 26 2022
STATUS
approved