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A376814 a(n) is the number of squares that have all digits distinct in base n.

%I A376814 #37 Oct 31 2024 10:41:07
%S A376814 2,2,7,7,21,42,71,268,611,1352,3099,8471,23877,63564,182771,527001,
%T A376814 1671752,5055853
%N A376814 a(n) is the number of squares that have all digits distinct in base n.
%e A376814 a(4) = 7 because the only squares with distinct digits in base 4 are 0^2 = 0_4, 1^2 = 1_4, 2^2 = 10_4, 3^2 = 21_4, 6^2 = 210_4, 7^2 = 301_4 and 15^2 = 3201_4.
%p A376814 f:= proc(b) local k,t,F;
%p A376814  t:= 0;
%p A376814  for k from 0 to floor(sqrt(b^b-1)) do
%p A376814    F:= convert(k^2, base, b);
%p A376814    if nops(F) = nops(convert(F,set)) then t:= t+1 fi;
%p A376814  od;
%p A376814  t
%p A376814 end proc:
%p A376814 map(f, [$2..12]);
%o A376814 (Python)
%o A376814 from math import isqrt
%o A376814 from sympy.ntheory import digits
%o A376814 def A376814(n): return sum(1 for k in range(isqrt(n**n-1)+1) if len(s:=digits(k**2,n)[1:])==len(set(s))) # _Chai Wah Wu_, Oct 09 2024
%Y A376814 Cf. A119509, A376897.
%K A376814 nonn,base,more
%O A376814 2,1
%A A376814 _Robert Israel_, Oct 09 2024
%E A376814 a(15)-a(16) from _Michael S. Branicky_, Oct 09 2024
%E A376814 a(17) from _Michael S. Branicky_, Oct 10 2024
%E A376814 a(18) from _Michael S. Branicky_, Oct 14 2024
%E A376814 a(19) from _Michael S. Branicky_, Oct 31 2024