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

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, 70, 72, 80, 81, 84, 90, 100, 102, 108, 111, 117, 120, 126, 135, 144, 153, 162, 171, 180, 200, 201, 204, 207, 210, 216, 222, 225, 234, 240, 243, 252, 261, 270, 288

Offset: 1

Author

Jayanta Basu, May 15 2013

Keywords

• nonn
• base

Comments

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

From Robert Israel, May 11 2017: (Start)

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.

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

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)

Examples

			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.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Maple

filter:= proc(n) local s,L;
     L:= convert(n,base,10);
     s:= convert(L,`+`);
     n mod s = 0 and nops({seq(9*d mod s, d = L)}) = 1
end proc:
select(filter, [$1..1000]); # Robert Israel, May 11 2017

Mathematica

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