A096093 - OEIS

%I #9 Jun 01 2020 20:47:38

%S 105,108,405,702,703,1001,1005,1008,1053,2002,2016,2025,2079,2106,

%T 3003,3024,3042,3045,3105,3402,4004,4005,5005,5049,6006,6031,6045,

%U 6048,6072,6075,6084,6105,6804,7007,7011,7128,7425,8008,8019,8092,8316,8712,9009

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

%H Robert Israel, <a href="/A096093/b096093.txt">Table of n, a(n) for n = 1..1000</a>

%e 105 is a term as 015 is a proper divisor of 105.

%e 2178 is a proper divisor of 8712 and 8712/2178=4.

%e 1089 is a proper divisor of 9801 and 9801/1089=9.

%p filter:= proc(n) local L,nL,P;

%p   L:= convert(n,base,10);

%p   nL:= nops(L);

%p   P:= subs(L=NULL, combinat:-permute(L));

%p   ormap(p -> n mod add(p[i]*10^(i-1),i=1..nL) = 0, P)

%p end proc:

%p select(filter, [seq(seq(10*i+j,j=1..9),i=1..10000)]); # _Robert Israel_, Jun 01 2020

%t 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 *)

%Y Cf. A096092.

%K base,nonn

%O 1,1

%A _Amarnath Murthy_, Jun 22 2004

%E Edited, corrected and extended by _Robert G. Wilson v_, Jun 23 2004