login
A225782
Numbers such that every permutation of digits of n is divisible by sum of digits of n.
1
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
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
KEYWORD
nonn,base
AUTHOR
Jayanta Basu, May 15 2013
STATUS
approved