A131417 Numbers n such that Sum_digits(n)=Sum_digits[n*Sum_digits(n)].

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

Offset: 1

Author

Paolo P. Lava and Giorgio Balzarotti, Jul 09 2007

Keywords

• easy
• nonn
• base

Examples

			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.
		

Crossrefs

Cf. A007953, A131418.

Programs

Maple

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);

Mathematica

sdQ[n_]:=Module[{c=Total[IntegerDigits[n]]},c==Total[ IntegerDigits[ c n]]]; Select[Range[0,350],sdQ] (* Harvey P. Dale, Nov 13 2011 *)

PARI

isok(n) = my(sn = sumdigits(n)); sn == sumdigits(n*sn); \\ Michel Marcus, May 10 2019