OFFSET
1,1
COMMENTS
a(n) = 0, for n > 10.
LINKS
EXAMPLE
a(1)=3 because all three 1-digit squares, 1, 4, and 9, have trivially distinct digits.
a(2)=6 because all six 2-digit squares, 16, 25, 36, 49, 64, and 81, have distinct digits.
158407396 = 12586^2: has 9 distinct digits. Thus, this number contributes to a(9). On the other hand, 158382225 = 12585^2 has repeated digits. Thus, it doesn't contribute.
MATHEMATICA
Table[Length[Select[Range[100000], Length[Union[IntegerDigits[#^2]]] == k && Length[IntegerDigits[#^2]] == k &]], {k, 10}]
PROG
(Python)
from math import isqrt
from itertools import permutations
def sqr(n): return isqrt(n)**2 == n
def a(n):
if n > 10: return 0
return sum(1 for p in permutations("0123456789", n) if p[0] != '0' and sqr(int("".join(p))))
print([a(n) for n in range(1, 31)]) # Michael S. Branicky, Oct 29 2023
CROSSREFS
KEYWORD
nonn,base,easy
AUTHOR
Tanya Khovanova, Oct 29 2023
STATUS
approved