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A046019 a(n) gives the number of different powers m^n for which the sum of the digits is equal to m. 8
1, 9, 2, 6, 6, 5, 5, 9, 4, 4, 7, 4, 2, 12, 6, 8, 7, 5, 3, 10, 4, 4, 8, 4, 4, 14, 5, 3, 7, 6, 2, 11, 2, 8, 4, 6, 3, 9, 3, 3, 7, 2, 5, 10, 6, 4, 9, 9, 5, 12, 2, 4, 5, 5, 6, 3, 2, 7, 4, 5, 5, 6, 3, 4, 5, 5, 4, 9, 2, 6, 4, 3, 3, 6, 5, 6, 4, 4, 5, 9, 5, 3, 5, 5, 2, 6, 3, 7, 7, 4, 3, 8, 4, 4, 9, 6, 2, 8, 2, 5, 6, 3 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of m >= 1 with m = sum of digits of m^n.

LINKS

T. D. Noe, Table of n, a(n) for n = 0..1000

FORMULA

a(n) = 1 + A046471(n). - T. D. Noe, Nov 26 2008

EXAMPLE

a(7)=9 because:

1^7=1

18^7= 612220032 and 6+1+2+2+2+3+2=18

27^7= 10460353203 and 1+4+6+3+5+3+2+3=27

31^7= 27512614111 and 2+7+5+1+2+6+1+4+1+1+1=31

34^7= 52523350144 and 5+2+5+2+3+3+5+1+4+4=34

43^7= 271818611107 and 2+7+1+8+1+8+6+1+1+1+7=43

53^7= 1174711139837 and 1+1+7+4+7+1+1+1+3+9+8+3+7=53

58^7= 2207984167552 and 2+2+7+9+8+4+1+6+7+5+5+2=58

68^7= 6722988818432 and 6+7+2+2+9+8+8+8+1+8+4+3+2=68

a(9)=4 because:

1^9=1

54^9=3904305912313344 and 3+9+4+3+5+9+1+2+3+1+3+3+4+4=54

71^9=45848500718449031 and 4+5+8+4+8+5+7+1+8+4+4+9+3+1=71

81^9=150094635296999121 and 1+5+9+4+6+3+5+2+9+6+9+9+9+1+2+1=81

CROSSREFS

Cf. A124359, A152147 (table of m such that the sum of digits of m^n equals m)

Sequence in context: A160262 A107821 A154162 * A021523 A275647 A011436

Adjacent sequences:  A046016 A046017 A046018 * A046020 A046021 A046022

KEYWORD

nonn,base

AUTHOR

David W. Wilson

EXTENSIONS

Examples provided by Paolo P. Lava, Oct 30 2006

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, May 27 2007

STATUS

approved

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Last modified August 22 16:37 EDT 2019. Contains 326179 sequences. (Running on oeis4.)