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A096093 Numbers, not divisible by 10, whose digits can be permuted to get a proper divisor. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
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
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Jun 22 2004
EXTENSIONS
Edited, corrected and extended by Robert G. Wilson v, Jun 23 2004
STATUS
approved

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Last modified June 21 06:38 EDT 2024. Contains 373540 sequences. (Running on oeis4.)