A023106 a(n) is a power of the sum of its digits.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 81, 512, 2401, 4913, 5832, 17576, 19683, 234256, 390625, 614656, 1679616, 17210368, 34012224, 52521875, 60466176, 205962976, 612220032, 8303765625, 10460353203, 24794911296, 27512614111, 52523350144, 68719476736

Offset: 0

Author

David W. Wilson

Keywords

• nonn
• base
• nice

Comments

Base-10 Reacher numbers: named for the character Jack Reacher in the series of books by Lee Child. Reacher likes the number 81 because it is the square of the sum of its base-10 digits. - Jeffrey Shallit, Apr 03 2015

Contains A061209 and A061210 and all terms of A061211. See A252648 for numbers which are the sum of some power of their digits. - M. F. Hasler, Apr 13 2015

Examples

			2401 is an element because 2401 = 7^4 is a power of its digit sum 7.
		

References

• Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 36.

Links

• David W. Wilson, Table of n, a(n) for n = 0..1137
• Jeffrey Shallit, Mathematics in a Jack Reacher Novel, blog post, September 8 2007.

Crossrefs

Cf. A061209, A061210, A061211, A252648.

Programs

Mathematica

fQ[n_] := Block[{b = Plus @@ IntegerDigits[n]}, If[b > 1, IntegerQ[ Log[b, n]] ]]; Take[ Select[ Union[ Flatten[ Table[n^m, {n, 55}, {m, 9}]]], fQ[ # ] &], 31] (* Robert G. Wilson v, Jan 28 2005 *)
Join[{0,1},Select[Range[0,1700000],IntegerQ[Log[Total[IntegerDigits[#]],#]]&]//Quiet] (* The program generates the first 21 terms of the sequence. *) (* Harvey P. Dale, Mar 30 2024 *)

PARI

is(n)={n<10||(!(n%s=sumdigits(n))&&s>1&&n==s^round(log(n)/log(s)))} \\ M. F. Hasler, Apr 13 2015

Python

import math
def is_valid(n): dsum = sum(map(int, str(n))); return dsum ** int(round(math.log(n, dsum))) == n if dsum > 1 else n < 2
# Victor Dumbrava, May 02 2018