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A135195
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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=10.
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17
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6, 330, 360, 1230, 1440, 2250, 2490, 2970, 3150, 3300, 3600, 4410, 5010, 5310, 6930, 8460, 10020, 12300, 12840, 12852, 13050, 14400, 14700, 15420, 15840, 16500, 17220, 18480, 20010, 21840, 22500, 23310, 24840, 24900, 27702, 28050, 29610, 29700, 31500
(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)=11.
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EXAMPLE
| 6^1=6 is a multiple of Sum_digits(6)=6
6^2=36 is a multiple of Sum_digits(36)=9
6^3=216 is a multiple of Sum_digits(216)=9
6^4=1296 is a multiple of Sum_digits(1296)=18
6^5=7776 is a multiple of Sum_digits(7776)=27
6^6=46656 is a multiple of Sum_digits(46656)=27
6^7=279936 is a multiple of Sum_digits(279936)=36
6^8=1679616 is a multiple of Sum_digits(1679616)=36
6^9=10077696 is a multiple of Sum_digits(10077696)=36
6^10=60466176 is a multiple of Sum_digits(60466176)=36
6^11=362797056 is not a multiple of Sum_digits(362797056)=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(15000, 10);
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CROSSREFS
| Cf. A135186, A135187, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
Sequence in context: A135397 A042421 A003742 * A001509 A003031 A144849
Adjacent sequences: A135192 A135193 A135194 * A135196 A135197 A135198
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KEYWORD
| nonn,base
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AUTHOR
| Paolo P. Lava & Giorgio Balzarotti (paoloplava(AT)gmail.com), Nov 23 2007
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EXTENSIONS
| Example corrected by Paolo P. Lava (paoloplava(AT)gmail.com), Oct 23 2009
More terms from Max Alekseyev (maxale(AT)gmail.com), Sep 24 2011
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