cp's OEIS Frontend

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

%I A046019 #18 Sep 24 2018 16:53:13
%S A046019 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,
%T A046019 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,
%U A046019 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
%N A046019 a(n) gives the number of different powers m^n for which the sum of the digits is equal to m.
%C A046019 Number of m >= 1 with m = sum of digits of m^n.
%H A046019 T. D. Noe, <a href="/A046019/b046019.txt">Table of n, a(n) for n = 0..1000</a>
%F A046019 a(n) = 1 + A046471(n). - _T. D. Noe_, Nov 26 2008
%e A046019 a(7)=9 because:
%e A046019 1^7=1
%e A046019 18^7= 612220032 and 6+1+2+2+2+3+2=18
%e A046019 27^7= 10460353203 and 1+4+6+3+5+3+2+3=27
%e A046019 31^7= 27512614111 and 2+7+5+1+2+6+1+4+1+1+1=31
%e A046019 34^7= 52523350144 and 5+2+5+2+3+3+5+1+4+4=34
%e A046019 43^7= 271818611107 and 2+7+1+8+1+8+6+1+1+1+7=43
%e A046019 53^7= 1174711139837 and 1+1+7+4+7+1+1+1+3+9+8+3+7=53
%e A046019 58^7= 2207984167552 and 2+2+7+9+8+4+1+6+7+5+5+2=58
%e A046019 68^7= 6722988818432 and 6+7+2+2+9+8+8+8+1+8+4+3+2=68
%e A046019 a(9)=4 because:
%e A046019 1^9=1
%e A046019 54^9=3904305912313344 and 3+9+4+3+5+9+1+2+3+1+3+3+4+4=54
%e A046019 71^9=45848500718449031 and 4+5+8+4+8+5+7+1+8+4+4+9+3+1=71
%e A046019 81^9=150094635296999121 and 1+5+9+4+6+3+5+2+9+6+9+9+9+1+2+1=81
%Y A046019 Cf. A124359, A152147 (table of m such that the sum of digits of m^n equals m)
%K A046019 nonn,base
%O A046019 0,2
%A A046019 _David W. Wilson_
%E A046019 Examples provided by _Paolo P. Lava_, Oct 30 2006
%E A046019 Edited by _N. J. A. Sloane_ at the suggestion of _Andrew S. Plewe_, May 27 2007