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A023106 a(n) is a power of the sum of its digits. 6
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
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 *)
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 *)
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
Sequence in context: A193757 A246605 A038178 * A135480 A289979 A228326
KEYWORD
nonn,base,nice
AUTHOR
STATUS
approved

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Last modified June 19 09:37 EDT 2024. Contains 373501 sequences. (Running on oeis4.)