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A135189
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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=4.
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17
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18, 48, 110, 111, 234, 306, 342, 396, 486, 576, 756, 792, 1010, 1100, 1120, 1164, 1404, 1548, 1566, 1740, 1854, 2106, 2160, 2376, 2430, 2502, 2592, 2640, 2754, 2790, 2850, 2880, 3006, 3060, 3072, 3078, 3180, 3330, 3366, 3420, 3510, 3564, 3690
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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FORMULA
| Positive integers n such that A195860(n)=5.
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EXAMPLE
| 18^1=18 -> Sum_digits(18)=9 and 18 is a multiple of 9.
18^2=324 -> Sum_digits(324)=9 and 324 is a multiple of 9.
18^3=5832 -> Sum_digits(5832)=18 and 5832 is a multiple of 18.
18^4=104976 -> Sum_digits(104976)=27 and 104976 is a multiple of 27
18^5=1889568 -> Sum_digits(1889568)=45 and 1889568 is not a multiple of 45.
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MAPLE
| 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(2000, 4);
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CROSSREFS
| Cf. A135186, A135187, A135188, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
Sequence in context: A099119 A105520 A067726 * A178398 A071365 A097319
Adjacent sequences: A135186 A135187 A135188 * A135190 A135191 A135192
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KEYWORD
| nonn,base
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Nov 22 2007
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EXTENSIONS
| More terms from Max Alekseyev (maxale(AT)gmail.com), Sep 24 2011
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