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A131417
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Numbers n such that Sum_digits(n)=Sum_digits[n*Sum_digits(n)].
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2
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0, 1, 9, 10, 18, 19, 27, 28, 36, 37, 45, 46, 55, 64, 73, 82, 90, 91, 99, 100, 109, 117, 118, 126, 127, 135, 136, 145, 154, 163, 172, 180, 181, 190, 198, 199, 208, 217, 225, 226, 234, 235, 244, 253, 262, 270, 271, 280, 288, 289, 297, 298, 307, 316, 325, 334, 343
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OFFSET
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1,3
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LINKS
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EXAMPLE
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n=271 --> 2+7+1=10 --> 271*10=2710 and 2+7+1+0=10.
n=468 --> 4+6+8=18 --> 468*18=8424 and 8+4+2+4=18.
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MAPLE
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P:=proc(n) local a, i, k, w; for i from 0 by 1 to n do w:=0; k:=i; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; a:=w; k:=i*w; w:=0; while k>0 do w:=w+k-(trunc(k/10)*10); k:=trunc(k/10); od; if a=w then print(i); fi; od; end: P(1000);
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MATHEMATICA
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sdQ[n_]:=Module[{c=Total[IntegerDigits[n]]}, c==Total[ IntegerDigits[ c n]]]; Select[Range[0, 350], sdQ] (* Harvey P. Dale, Nov 13 2011 *)
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PROG
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(PARI) isok(n) = my(sn = sumdigits(n)); sn == sumdigits(n*sn); \\ Michel Marcus, May 10 2019
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CROSSREFS
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KEYWORD
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easy,nonn,base
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AUTHOR
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STATUS
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approved
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