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Search: id:A135193
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| A135193 |
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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=8. |
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+0
17
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| 180, 252, 720, 1350, 1800, 2040, 2520, 3324, 3870, 5520, 6552, 6750, 7200, 7812, 8220, 8280, 8964, 9450
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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180^1=180 is a multiple of Sum_digits(180)=9
180^2=32400 is a multiple of Sum_digits(32400)=9
180^3=5832000 is a multiple of Sum_digits(5832000)=18
180^4=1049760000 is a multiple of Sum_digits(1049760000)=27
180^5=188956800000 is a multiple of Sum_digits(188956800000)=45
180^6=34012224000000 is a multiple of Sum_digits(34012224000000)=18
180^7=6122200320000000 is a multiple of Sum_digits(6122200320000000)=18
180^8=1101996057600000000 is a multiple of Sum_digits(1101996057600000000)=45
180^9=198359290368000000000 is not a multiple of Sum_digits(198359290368000000000)=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(10000, 8);
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CROSSREFS
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Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
Sequence in context: A068403 A030636 A160134 this_sequence A095650 A066164 A008891
Adjacent sequences: A135190 A135191 A135192 this_sequence A135194 A135195 A135196
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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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