%I A126789
%S A126789 1,36,66,88,257,268,279,448,369,459,0,666,0,578,579,678,0,1689,0,2558,
%T A126789 789,0,0,1899,13557,0,999,3477,0,2589,0,2688,0,0,13578,3489,0,0,0,3588,
%U A126789 0,2799,0,0,4569,0,0,4668,4677,5568,0,0,0,3699,0,3789,0,0,0,4599,0,0
%N A126789 a(n) is the smallest number such that the product of its digits is n 
               times the sum of its digits, or 0 if no such number exists.
%C A126789 a(11) = 0. Proof: 11 is a prime number and the product of digits of a 
               number in base 10 can never be a multiple of 11. - Stefan Steinerberger 
               (stefan.steinerberger(AT)gmail.com), Jun 07 2007
%C A126789 More generally, a(n) = 0 for all n which are divisible by a prime bigger 
               than 7. This means that the sequence will almost always be 0 (with 
               the set of exceptions having density 0). In each term the digits 
               will be increasing (otherwise we could rearrange the digits so that 
               they form a smaller number with the requested property). If all prime 
               factors of n do not exceed 7, does this mean that the a(n) is not 
               0? - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Jun 
               14 2007
%e A126789 a(2)=36 because 3*6/(3+6)=2 and no number smaller than 36 has this property.
%p A126789 for n from 1 to 10 do b:=proc(k) local kk: kk:=convert(k,base,10): if 
               product(kk[j],j=1..nops(kk))=n*sum(kk[j],j=1..nops(kk)) then k else 
               fi end: a[n]:=[seq(b(k),k=1..1000)][1]: od: seq(a[n],n=1..10); # 
               program works only for n from 1 to 10 - Emeric Deutsch (deutsch(AT)duke.poly.edu), 
               Mar 07 2007
%t A126789 a[1] := 1; a[n_] := Module[{}, k = 0; If[FactorInteger[n][[ -1, 1]] < 
               8, k = 1; While[Times @@ IntegerDigits[k] != n*Plus @@ IntegerDigits[k], 
               k++ ]]; k]; Table[a[i], {i, 1, 80}] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Jun 14 2007
%Y A126789 This sequence is a subsequence of A061013 (Product of digits of n) is 
               divisible by (sum of digits of n), where 0's are not permitted.
%Y A126789 Sequence in context: A082295 A060671 A074315 this_sequence A068144 A036785 
               A114127
%Y A126789 Adjacent sequences: A126786 A126787 A126788 this_sequence A126790 A126791 
               A126792
%K A126789 base,nonn
%O A126789 1,2
%A A126789 Tanya Khovanova (tanyakh(AT)yahoo.com), Feb 19 2007
%E A126789 More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 07 2007
%E A126789 More terms from Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), 
               Jun 14 2007