A061510 Write n in decimal, omit 0's, raise each digit k to k-th power and multiply.

1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 1, 1, 4, 27, 256, 3125, 46656, 823543, 16777216, 387420489, 4, 4, 16, 108, 1024, 12500, 186624, 3294172, 67108864, 1549681956, 27, 27, 108, 729, 6912, 84375, 1259712, 22235661, 452984832, 10460353203

Offset: 0

Author

Amarnath Murthy, May 06 2001

Keywords

• base
• look
• nonn

Comments

The empty product is 1. If one accepts 0^0 = 1, then "omit 0's" is unnecessary. - Michael S. Branicky, Nov 26 2024

Examples

			a(4) = 4^4 = 256.
a(123) =  1^1 * 2^2 * 3^3 = 108.
a(1024) = 1^1 * 2^2 * 4^4 = 1024.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 0..10000
• Wikipedia, Zero to the power of zero

Crossrefs

Cf. A061509.

Programs

Maple

a:= n-> mul(i^i,i=convert(n, base, 10)):
seq(a(n), n=0..39);  # Alois P. Heinz, Nov 26 2024

Mathematica

A061510[n_] := If[n == 0, 1, Times @@ (#^#) & [DeleteCases[IntegerDigits[n], 0]]];
Array[A061510, 50, 0] (* Paolo Xausa, Nov 26 2024 *)

PARI

a(n) = my(d=digits(n)); vecprod(vector(#d, k, d[k]^d[k])); \\ Michel Marcus, Nov 25 2024

Python

from math import prod
def a(n): return prod(d**d for d in map(int, str(n)) if d > 1)
print([a(n) for n in range(40)]) # Michael S. Branicky, Nov 25 2024

Extensions

Corrected and extended by Matthew Conroy, May 13 2001