|
%I #7 Dec 06 2012 18:27:00
%S 1,6,10,11,15,19,20,22,24,30,31,33,35,42,51,52,60,62,66,68,71,79,87,
%T 90,100,101,102,103,104,105,109,110,112,114,118,120,123,124,130,132,
%U 136,138,141,143,145,147,150,153,160,161,165,167,168,174,177,190,194,198
%N Numbers n for which the sum of their digits divides sigma(n).
%H Harvey P. Dale, <a href="/A132628/b132628.txt">Table of n, a(n) for n = 1..1000</a>
%e n=147 -> sigma(n)=1+3+7+21+49+147=228 Sum_digits(n)=1+4+7=12 -> 228/12 = 19
%e n=177 -> sigma(n)=1+3+59+177=240 Sum_digits(n)=1+7+7=15 -> 240/15 = 16
%p with(numtheory); P:=proc(n) local a,i,j,k,w; for i from 1 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; j:=sigma(i)/w; if trunc(j)=j then print(i,j); fi; od; end: P(200)
%t Select[Range[200],Divisible[DivisorSigma[1,#],Total[IntegerDigits[#]]]&] (* _Harvey P. Dale_, Dec 06 2012 *)
%Y Cf. A007691, A054030, A132629.
%K nonn,base,easy
%O 1,2
%A _Paolo P. Lava_ and _Giorgio Balzarotti_, Aug 24 2007
|
