A225780 -id:A225780 - cp's OEIS frontend

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

Jayanta Basu, May 15 2013

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)

			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.

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

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

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

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

A334249 Numbers k such that (k - digitsum(k))(k + digitsum(k)) contains k as a substring.

Original entry on oeis.org

11, 88, 101, 448, 673, 776, 1001, 2879, 3553, 9537, 10001, 14651, 36559, 49056, 51073, 54116, 59600, 100001, 505025, 998999, 1000001, 4115964, 5050250, 5133355, 10000001, 10050125, 19349727, 26550976, 33726078, 35792647, 42349456, 43605459, 50050025, 66952741, 88027284, 88819024, 100000001, 105124922

Offset: 1

Scott R. Shannon, May 05 2020

All numbers of the form 10^n + 1 (for n > 0) are in the sequence.

			11 is a term as digitsum(11) = 2 and (11 - 2)(11 + 2) = 117, which contains '11' as a substring.
9537 is a term as digitsum(9537) = 24 and (9537 - 24)(9537 + 24) = 90953793, which contains '9537' as a substring.

Giovanni Resta, Table of n, a(n) for n = 1..95

Cf. A007953, A257784, A125526, A082208, A225780.

cp's OEIS Frontend

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

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