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A378246 Integers that are equal to the product of their nonzero digits raised to their own power.

%I A378246 #56 Dec 14 2024 20:39:40
%S A378246 1,1024,12500
%N A378246 Integers that are equal to the product of their nonzero digits raised to their own power.
%C A378246 If one accepts 0^0 = 1, the "nonzero" part of the description is unnecessary.
%C A378246 From _Michael S. Branicky_, Nov 25 2024: (Start)
%C A378246 Terms must be 7-smooth (A002473).
%C A378246 a(4) > 10^200 if it exists. (End)
%H A378246 Jason Hammerman, <a href="/A378246/a378246.py.txt">Python program</a>
%H A378246 Wikipedia, <a href="https://en.wikipedia.org/wiki/Zero_to_the_power_of_zero">Zero to the power of zero</a>
%e A378246 1024  = 1^1 * 2^2 * 4^4.
%e A378246 12500 = 1^1 * 2^2 * 5^5.
%t A378246 F[a_]:=If[a==0,1,a^a];Select[Range[10^5],#==Times@@F/@IntegerDigits[#]&] (* _James C. McMahon_, Dec 14 2024 *)
%o A378246 (Python) # See Python program link.
%o A378246 (Python)
%o A378246 from math import prod
%o A378246 def ok(n): return n == prod(d**d for d in map(int, str(n)) if d > 1)
%o A378246 print([k for k in range(10**5) if ok(k)]) # _Michael S. Branicky_, Nov 24 2024
%o A378246 (PARI) isok(k) = my(d=digits(k)); k == vecprod(vector(#d, i, d[i]^d[i])); \\ _Michel Marcus_, Nov 22 2024
%Y A378246 Fixed points of A061510.
%Y A378246 Inspired by A046253.
%Y A378246 Cf. A002473.
%K A378246 nonn,base,bref,more
%O A378246 1,2
%A A378246 _Jason Hammerman_, Nov 20 2024