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A135187
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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=2.
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17
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9, 21, 45, 63, 117, 132, 140, 144, 190, 201, 204, 207, 220, 243, 264, 288, 315, 333, 402, 414, 441, 460, 476, 506, 513, 531, 550, 552, 594, 603, 621, 648, 666, 702, 770, 774, 828, 846, 864, 880, 954, 999, 1012, 1017, 1032, 1044, 1053, 1056, 1062
(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)=3.
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EXAMPLE
| 9^1=9; 9^2=81 -> Sum_digits(81)=9 is a multiple of 9.
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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, 2);
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CROSSREFS
| Cf. A135186, A135188, A135189, A135190, A135191, A135192, A135193, A135194, A135195, A135196, A135197, A135198, A135199, A135200, A135201, A135202.
Sequence in context: A154862 A020137 A020190 * A173391 A133762 A160414
Adjacent sequences: A135184 A135185 A135186 * A135188 A135189 A135190
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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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