A046019 a(n) gives the number of different powers m^n for which the sum of the digits is equal to m.

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

Author

David W. Wilson

Keywords

• nonn
• base

Comments

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

Examples

			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
		

Links

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

Crossrefs

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

Formula

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

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