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%I #35 Sep 03 2016 16:57:13
%S 1,2,3,4,5,6,7,8,9,11,13,15,17,19,20,22,24,26,28,31,33,35,37,39,40,42,
%T 44,46,48,51,53,55,57,59,60,62,64,66,68,71,73,75,77,79,80,82,84,86,88,
%U 91,93,95,97,99,100,101,102,103,104,105,106,107,108,109,110,111
%N Numbers n such that the average of different permutations of digits of n is an integer.
%C Complement of A273492.
%C Permutations with a first digit of 0 are included in the average (i.e. 0010 is taken to be 10, 01 is taken to be 1, etc.).
%C From _Robert Israel_, Sep 01 2016: (Start)
%C n such that A002275(A055642(n))*A007953(n) is divisible by A055642(n).
%C In particular, contains all k-digit numbers if k is in A014950. (End)
%H Robert Israel, <a href="/A275945/b275945.txt">Table of n, a(n) for n = 1..10000</a>
%e 97 is a term because (97+79) is divisible by 2.
%e 100 is a term because (1+10+100) is divisible by 3.
%e 123 is a term because (123+132+213+231+312+321) is divisible by 6.
%e 1001 is not a term because (11+101+110+1001+1010+1100) is not divisible by 6.
%p f:= proc(n) local L, d, s;
%p L:= convert(n, base, 10);
%p d:= nops(L);
%p s:= convert(L, `+`);
%p evalb(s*(10^d-1)/9 mod d = 0)
%p end proc:
%p select(f, [$1..10000]); # _Robert Israel_, Sep 01 2016
%t Select[Range@ 111, IntegerQ@ Mean@ Map[FromDigits, Permutations@ #] &@ IntegerDigits@ # &] (* _Michael De Vlieger_, Aug 29 2016 *)
%o (PARI) A055642(n) = #Str(n);
%o A007953(n) = sumdigits(n);
%o for(n=1, 2000, if((((10^A055642(n)-1)/9)*A007953(n)) % A055642(n) == 0, print1(n, ", ")));
%Y Cf. A002275, A014950, A045876, A055642, A066642, A007953, A273492.
%K easy,base,nonn
%O 1,2
%A _Altug Alkan_, Aug 29 2016
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