This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A357755 #28 Mar 23 2025 20:53:21 %S A357755 3265920,468372,65663,15487,5020,1930,855,417,246,114,97,45,33,24,20, %T A357755 18,7,6,1,3,2,3,0,1,0,2,0,0,0,0,0,0,0,0,1,0,0,1 %N A357755 Number of solutions for a 10-digit number whose n-th power contains each digit (0-9) exactly n times. %C A357755 A number with 10*n digits may have all ten digits (0-9) repeated n times. The probability of this is (10*n)!/((n!)^10 * (10^(10*n)-10^(10*n-1))). There are 10^10-10^(10-1/n) numbers which are n-th powers of 10-digit numbers. So there may exist Count = (10*n)!*(10^10-10^(10-1/n))/((n!)^10 * (10^(10*n)-10^(10*n-1))) numbers with the desired property. %C A357755 No solutions were found for n = 39 to 1000. %e A357755 a(20) = 3 because there are 3 10-digit numbers (8951993472, 9921107394, and 9985819785) whose 20th power contains each digit (0-9) 20 times. %o A357755 (Python) %o A357755 def flag(p, n): %o A357755 return all(p.count(d) == n for d in "0123456789") %o A357755 def a(n): %o A357755 num=0 %o A357755 for i in range(10**10-1, 3*int(10**(10-1/n)/3), -3): %o A357755 if flag(str(i**n), n): %o A357755 num+=1 %o A357755 return(num) %Y A357755 Cf. A010784, A078255, A154532, A154566. %K A357755 nonn,base,more %O A357755 1,1 %A A357755 _Zhining Yang_, Nov 26 2022