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Search: id:A135194
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| A135194 |
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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=9. |
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+0
17
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| 240, 270, 450, 630, 840, 1050, 2340, 2400, 2610, 2700, 3024, 3036, 3990, 4500, 5292, 6300, 6390, 8400, 9990, 10170, 10500
(list; graph; listen)
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OFFSET
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1,1
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EXAMPLE
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240^1=240 is a multiple of Sum_digits(240)=6.
240^2=57600 is a multiple of Sum_digits(240)=18.
240^3=13824000 is a multiple of Sum_digits(13824000)=18.
240^4=3317760000 is a multiple of Sum_digits(3317760000)=27.
240^5=796262400000 is a multiple of Sum_digits(796262400000)=36.
240^6=191102976000000 is a multiple of Sum_digits(191102976000000)=36.
240^7=45864714240000000 is a multiple of Sum_digits(45864714240000000)=45.
240^8=11007531417600000000 is a multiple of Sum_digits(11007531417600000000)=36.
240^9=2641807540224000000000 is a multiple of Sum_digits(2641807540224000000000)=45.
240^10=634033809653760000000000 is not a multiple of Sum_digits(634033809653760000000000)=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(15000, 9);
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CROSSREFS
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Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
Sequence in context: A100748 A072235 A121378 this_sequence A031173 A067373 A030638
Adjacent sequences: A135191 A135192 A135193 this_sequence A135195 A135196 A135197
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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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