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A225782 Numbers such that every permutation of digits of n is divisible by sum of digits of n.

%I A225782 #9 May 12 2017 00:51:03
%S A225782 1,2,3,4,5,6,7,8,9,10,12,18,20,21,24,27,30,36,40,42,45,48,50,54,60,63,
%T A225782 70,72,80,81,84,90,100,102,108,111,117,120,126,135,144,153,162,171,
%U A225782 180,200,201,204,207,210,216,222,225,234,240,243,252,261,270,288
%N A225782 Numbers such that every permutation of digits of n is divisible by sum of digits of n.
%C A225782 Subsets of both A005349 and A225780. First member of A225780 missing here is 209. Next one is 308.
%C A225782 From _Robert Israel_, May 11 2017: (Start)
%C A225782 Numbers n such that n is divisible by A007953(n) and 9*d (mod A007953(n)) are all equal for all digits d of n.
%C A225782 If n is in the intersection of this sequence and A011540, then so is 10*n.  In particular, the sequence is infinite.
%C A225782 If n is in the sequence and A007953(n) > 81, then n = d*A002275(r) where 1 <= d <= 9 and r is in A014950. (End)
%H A225782 Robert Israel, <a href="/A225782/b225782.txt">Table of n, a(n) for n = 1..10000</a>
%e A225782 126 is a member since 126, 162, 216, 261, 612 and 621 are all divisible by (1+2+6)=9. 209 is not a member since 29 is not divisible by (2+9)=11.
%p A225782 filter:= proc(n) local s,L;
%p A225782      L:= convert(n,base,10);
%p A225782      s:= convert(L,`+`);
%p A225782      n mod s = 0 and nops({seq(9*d mod s, d = L)}) = 1
%p A225782 end proc:
%p A225782 select(filter, [$1..1000]); # _Robert Israel_, May 11 2017
%t A225782 d[n_]:=IntegerDigits[n]; sod[n_]:=Total[d[n]]; t={}; Do[t1=Table[FromDigits[k],{k,Permutations[d[n]]}]; If[Select[t1,Mod[#,sod[n]]!=0 &]=={},AppendTo[t,n]],{n,288}]; t
%Y A225782 Cf. A002275, A005349, A007953, A011540, A014950, A225780.
%K A225782 nonn,base
%O A225782 1,2
%A A225782 _Jayanta Basu_, May 15 2013