A072408 Least number > 1 which equals n-th power of the sum of its digits in decimal base.

2, 81, 512, 2401, 17210368, 34012224, 612220032, 20047612231936, 3904305912313344, 13744803133596058624, 8007313507497959524352, 2518170116818978404827136, 81920000000000000, 2670419511272061205254504361, 2759031540715333904109053133443

Offset: 1

Author

Labos Elemer, Jun 17 2002

Keywords

• base
• nonn

Examples

			a(1) = 2 > 1;
a(9) = 3904305912313344 = 54^9 = (3+9+0+4+3+0+5+9+1+2+3+1+3+3+4+4)^9.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..274
• Leo Moser, Digits of Powers, Recreational Mathematics, Curiosa 145. Scripta Mathematica Vol. XIII, March-June 1947, Nos. 1-2, page 117.

Crossrefs

Cf. A007953, A046017, A072081-A072083.

Programs

Mathematica

Array[Block[{k = 2}, While[k^# != Total[IntegerDigits[k^#]]^#, k++]; k^#] &, 13] (* Michael De Vlieger, Nov 05 2020 *)

Formula

a(n) = Min{ x; x=SumDigit(x)^n} = Min{x; x=A007953(x)^n}

a(n) = A046017(n)^n. - Michael De Vlieger, Nov 05 2020