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Search: id:A135197
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| A135197 |
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Numbers n that raised to the powers from 1 to k (with k>=1) are multiple of the sum of their digits (n raised to k+1 must not be a multiple). Case k=12. |
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+0
17
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| 90, 120, 900, 1200, 3480, 4650, 5700, 7140, 9000, 12000, 13140, 13260, 21180, 21660
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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90^1=90 is multiple of Sum_digits(90)=9
90^2=8100 is multiple of Sum_digits(8100)=9
etc. till
90^12=282429536481000000000000 is multiple of Sum_digits(282429536481000000000000)=54
while
90^13=25418658283290000000000000 is not multiple of Sum_digits(25418658283290000000000000)=63
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MAPLE
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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(25000, 12);
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CROSSREFS
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Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135198, A135199, A135200, A135201, A135202.
Sequence in context: A039401 A044004 A078493 this_sequence A025371 A025362 A114826
Adjacent sequences: A135194 A135195 A135196 this_sequence A135198 A135199 A135200
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KEYWORD
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easy,nonn,base
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AUTHOR
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Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), Nov 23 2007
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