A096093 Numbers, not divisible by 10, whose digits can be permuted to get a proper divisor.

105, 108, 405, 702, 703, 1001, 1005, 1008, 1053, 2002, 2016, 2025, 2079, 2106, 3003, 3024, 3042, 3045, 3105, 3402, 4004, 4005, 5005, 5049, 6006, 6031, 6045, 6048, 6072, 6075, 6084, 6105, 6804, 7007, 7011, 7128, 7425, 8008, 8019, 8092, 8316, 8712, 9009

Offset: 1

Author

Amarnath Murthy, Jun 22 2004

Keywords

• base
• nonn

Examples

			105 is a term as 015 is a proper divisor of 105.
2178 is a proper divisor of 8712 and 8712/2178=4.
1089 is a proper divisor of 9801 and 9801/1089=9.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A096092.

Programs

Maple

filter:= proc(n) local L,nL,P;
  L:= convert(n,base,10);
  nL:= nops(L);
  P:= subs(L=NULL, combinat:-permute(L));
  ormap(p -> n mod add(p[i]*10^(i-1),i=1..nL) = 0, P)
end proc:
select(filter, [seq(seq(10*i+j,j=1..9),i=1..10000)]); # Robert Israel, Jun 01 2020

Mathematica

f[n_] := Union[ IntegerQ /@ Drop[ n/FromDigits /@ Permutations[IntegerDigits[n]], 1]][[ -1]]; Select[ Range[ 9015], Mod[ #, 10] != 0 && f[ # ] == True &] (* Robert G. Wilson v, Jun 23 2004 *)

Extensions

Edited, corrected and extended by Robert G. Wilson v, Jun 23 2004