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

1,1

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.

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

Example

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.

Mathematica

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

Crossrefs

Cf. A007953 (digit sum), A046017 (least k = digit_sum(k)^n), A072081-A072083.

For k = sumdigits(k)^m, see also: A061209 = A046459^3, A061210 = A055575^4, A254000 = A055576^5, A375343 = A055577^6, A023106 and table A152147 (any m > 1).

Sequence in context: A187858 A371508 A352742 * A318587 A302722 A123177

Adjacent sequences: A072405 A072406 A072407 * A072409 A072410 A072411

Keyword

base,nonn

Author

Labos Elemer, Jun 17 2002

Status

approved