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A023106 a(n) is a power of the sum of its digits. 5
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

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

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.

EXAMPLE

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

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 *)

PROG

(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

CROSSREFS

Cf. A061209, A061210, A061211, A252648.

Sequence in context: A193757 A246605 A038178 * A135480 A289979 A228326

Adjacent sequences:  A023103 A023104 A023105 * A023107 A023108 A023109

KEYWORD

nonn,base,nice

AUTHOR

David W. Wilson

STATUS

approved

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Last modified July 23 00:51 EDT 2018. Contains 312919 sequences. (Running on oeis4.)