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%I #12 Apr 07 2019 11:55:16
%S 60,150,600,1500,3390,4320,6000,9240,15000,33900,43200,51810,60000,
%T 92400,150000,288750,339000,432000,518100,600000,612150,686070,794640,
%U 924000,1043460,1122450,1225350,1305150,1483020,1500000,1711710,2125620,2174970
%N Numbers n that raised to the powers from 1 to k (with k>=1) are multiples of the sum of their digits (and n raised to k+1 must not be such a multiple). Case k=14.
%F Positive integers n such that A195860(n)=15.
%e 60^1=60 is multiple of Sum_digits(60)=6
%e 60^2=3600 is multiple of Sum_digits(3600)=9
%e ...
%e 60^14=7836416409600000000000000 is a multiple of Sum_digits(7836416409600000000000000)=54
%e while
%e 60^15=470184984576000000000000000 is not multiple of Sum_digits(470184984576000000000000000)=63
%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(30000,14);
%t msdQ[n_]:=Module[{b=Boole[Divisible[#,Total[IntegerDigits[#]]]&/@(n^Range[ 15])]}, Total[b]==14&&Last[b]==0]; Select[Range[22*10^5],msdQ] (* _Harvey P. Dale_, Apr 07 2019 *)
%Y Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135200, A135201, A135202.
%K nonn,base
%O 1,1
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Nov 26 2007
%E Terms a(10) onward from _Max Alekseyev_, Sep 24 2011
%E Definition clarified by _Harvey P. Dale_, Apr 07 2019
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