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Smallest number m such that m and the product of digits of m are both divisible by 2n, or 0 if no such number exists.

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`%I #14 Jun 21 2018 03:21:59
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`%S 2,4,6,8,0,168,378,48,36,0,0,168,0,476,0,288,0,1296,0,0,378,0,0,384,0,
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`%T 0,1296,728,0,0,0,448,0,0,0,1368,0,0,0,0,0,672,0,0,0,0,0,384,7742,0,0,
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`%U 0,0,1296,0,784,0,0,0,0,0,0,3276,2688,0,0,0,0,0,0,0,3168,0,0,0,0,0,0,0
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`%N Smallest number m such that m and the product of digits of m are both divisible by 2n, or 0 if no such number exists.
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`%C Here 0 is regarded as not divisible by any number.
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`%C a(n) = 0 if n is divisible by 5 or contains a prime divisor > 9. - _Sascha Kurz_, Aug 23 2002
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`%F a(n) = A085124(2*n). - _R. J. Mathar_, Jun 21 2018
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`%p f := 2:for i from 1 to 400 do b := ifactors(f*i)[2]: if b[nops(b)][1]>9 or (f*i mod 10) =0 then a[i] := 0:else j := 0:while true do j := j+f*i:c := convert(j,base,10): d := product(c[k],k=1..nops(c)): if (d mod f*i)=0 and d>0 then a[i] := j:break:fi: od:fi:od:seq(a[k],k=1..400);
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`%Y Cf. A073906, A085124, A073908, A073910, A073911, A073912.
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`%K nonn,base
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`%O 1,1
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`%A _Amarnath Murthy_, Aug 18 2002
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`%E More terms from _Sascha Kurz_, Aug 23 2002
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