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

1, 1024, 12500

Offset: 1

Author

Jason Hammerman, Nov 20 2024

Keywords

• nonn
• base
• bref
• more

Comments

If one accepts 0^0 = 1, the "nonzero" part of the description is unnecessary.

From Michael S. Branicky, Nov 25 2024: (Start)

Terms must be 7-smooth (A002473).

a(4) > 10^200 if it exists. (End)

Examples

			1024  = 1^1 * 2^2 * 4^4.
12500 = 1^1 * 2^2 * 5^5.
		

Links

• Jason Hammerman, Python program
• Wikipedia, Zero to the power of zero

Crossrefs

Fixed points of A061510.

Inspired by A046253.

Cf. A002473.

Programs

Mathematica

F[a_]:=If[a==0,1,a^a];Select[Range[10^5],#==Times@@F/@IntegerDigits[#]&] (* James C. McMahon, Dec 14 2024 *)

PARI

isok(k) = my(d=digits(k)); k == vecprod(vector(#d, i, d[i]^d[i])); \\ Michel Marcus, Nov 22 2024

Python

# See Python program link.

Python

from math import prod
def ok(n): return n == prod(d**d for d in map(int, str(n)) if d > 1)
print([k for k in range(10**5) if ok(k)]) # Michael S. Branicky, Nov 24 2024