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

1,2

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)

Links

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

Example

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.

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

Crossrefs

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

Sequence in context: A234474 A285829 A225780 * A235507 A235697 A085135

Adjacent sequences: A225779 A225780 A225781 * A225783 A225784 A225785

Keyword

nonn,base

Author

Jayanta Basu, May 15 2013

Status

approved