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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.
11
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
OFFSET
0,2
COMMENTS
Number of m >= 1 with m = sum of digits of m^n.
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 A335589 A275647
KEYWORD
nonn,base
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