A225782 - OEIS

%I #9 May 12 2017 00:51:03

%S 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 70,72,80,81,84,90,100,102,108,111,117,120,126,135,144,153,162,171,

%U 180,200,201,204,207,210,216,222,225,234,240,243,252,261,270,288

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

%C Subsets of both A005349 and A225780. First member of A225780 missing here is 209. Next one is 308.

%C From _Robert Israel_, May 11 2017: (Start)

%C 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 If n is in the intersection of this sequence and A011540, then so is 10*n.  In particular, the sequence is infinite.

%C 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 Robert Israel, <a href="/A225782/b225782.txt">Table of n, a(n) for n = 1..10000</a>

%e 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 filter:= proc(n) local s,L;

%p      L:= convert(n,base,10);

%p      s:= convert(L,`+`);

%p      n mod s = 0 and nops({seq(9*d mod s, d = L)}) = 1

%p end proc:

%p select(filter, [$1..1000]); # _Robert Israel_, May 11 2017

%t 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 Cf. A002275, A005349, A007953, A011540, A014950, A225780.

%K nonn,base

%O 1,2

%A _Jayanta Basu_, May 15 2013