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

1,1

Links

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

Example

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.

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 *)

Crossrefs

Cf. A096092.

Sequence in context: A260461 A090055 A090053 * A179142 A039553 A135999

Adjacent sequences: A096090 A096091 A096092 * A096094 A096095 A096096

Keyword

base,nonn

Author

Amarnath Murthy, Jun 22 2004

Extensions

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

Status

approved