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 A135202 Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sum of their digits (n raised to k+1 must not be a multiple). Case k=17. 17

%I

%S 3900,39000,390000,3900000,12432420,16528050,19211220,28845180,

%T 29549520,29895180,34310100,34899480,36659700,39000000,39159120,

%U 48452040,51092580,53295000,66156090,83393310,95416230,100960860,109052580,117865440,124324200

%N Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sum of their digits (n raised to k+1 must not be a multiple). Case k=17.

%F Positive integers n such that A195860(n)=18.

%e 3900^1=3900 is multiple of Sum_digits(3900)=12

%e 3900^2=15210000 is multiple of Sum_digits(3900^2)=9

%e ...

%e 3900^17 is a multiple of Sum_digits(3900^17)=108

%e while

%e 3900^18 is not multiple of Sum_digits(3900^18)=99

%p readlib(log10); P:=proc(n,m) local a,i,k,w,x,ok; for i from 1 by 1 to n do a:=simplify(log10(i)); if not (trunc(a)=a) then ok:=1; x:=1; while ok=1 do w:=0; k:=i^x; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if trunc(i^x/w)=i^x/w then x:=x+1; else if x-1=m then print(i); fi; ok:=0; fi; od; fi; od; end: P(50000,17);

%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201.

%K nonn,base

%O 1,1

%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 26 2007

%E Terms a(4) onward from _Max Alekseyev_, Sep 24 2011

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Last modified April 18 12:45 EDT 2021. Contains 343088 sequences. (Running on oeis4.)