%I A124053
%S A124053 7,18,45,61,72,85,90,145,270,306,315,367,376,448,477,540,547,585,667,
%T A124053 733,756,765,943,1152,1377,1899,1971,2106,2133,2155,2215,2224,2349,2628,
%U A124053 2822,2871,2968,3123,3139,3181,3204,3355,3546,3553,3775,3780,4455,4582
%N A124053 Numbers n that can be expressed as the sum of the digits of both m^k 
               and k^m for distinct numbers m and k which are not both equal to 
               powers of 10.
%C A124053 If "sumdigit" denotes the sum of the digits of a number then these are 
               the numbers n such that n=sumdigit(m^k)=sumdigit(k^m).
%C A124053 Two banal cases are not considered: 1) m=k because m^k=k^m and the sum 
               of the digits is authomatically equal for both the numbers; 2) powers 
               of 10 because sumdigit(10^a)=1 for any integer a. The same number 
               can be generated by different pairs: 477 cames from sumdigit(54^63)=sumdigit(63^54) 
               and sumdigit(90^120)=sumdigit(120^90) 2349 cames from sumdigit(216^222)=sumdigit(222^216), 
               sumdigit(216^225)=sumdigit(225^216) and sumdigit(219^222)=sumdigit(222^219)
%e A124053 270=sumdigit(36^39)=sumdigit(39^36)
%e A124053 1152=sumdigit(114^126)=sumdigit(126^114)
%e A124053 2133=sumdigit(204^213)=sumdigit(213^204)
%p A124053 P:=proc(n)local i,j,k,w,x,y; for i from 1 by 1 to n do for j from 1 by 
               1 to n do w:=0; x:=0; k:=i^j; y:=j^i; while k>0 do w:=w+k-trunc(k/
               10)*10; k:=trunc(k/10); od; while y>0 do x:=x+y-trunc(y/10)*10; y:=trunc(y/
               10); od; if (w=x) and (w<>1) and (i<j) then print(i,j,w); fi; od; 
               od; end: P(500);
%Y A124053 Cf. A124359, A124360, A046019, A124365, A124366, A124367.
%Y A124053 Sequence in context: A133673 A023166 A002764 this_sequence A084819 A019534 
               A024830
%Y A124053 Adjacent sequences: A124050 A124051 A124052 this_sequence A124054 A124055 
               A124056
%K A124053 nonn,base
%O A124053 1,1
%A A124053 Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 03 2006, Nov 
               29 2006