cp's OEIS Frontend

A073908 Smallest number m such that m and the product of digits of m are both divisible by 7n, or 0 if no such number exists.

%I A073908 #15 Jun 21 2018 03:21:13
%S A073908 7,378,273,476,175,378,3577,728,1197,0,0,672,0,7742,735,784,0,3276,0,
%T A073908 0,7497,0,0,7896,1575,0,7938,69776,0,0,0,12768,0,0,37975,3276,0,0,0,0,
%U A073908 0,71736,0,0,9765,0,0,8736,47677,0,0,0,0,7938,0,74872,0,0,0,0,0,0,7497
%N A073908 Smallest number m such that m and the product of digits of m are both divisible by 7n, or 0 if no such number exists.
%C A073908 Here 0 is regarded as not divisible by any number.
%C A073908 a(n) = 0 if n is divisible by 10 or contains a prime divisor > 9. - _Sascha Kurz_, Aug 23 2002
%F A073908 a(n) = A085124(7*n). - _R. J. Mathar_, Jun 21 2018
%e A073908 a(8) = 728 is divisible by 7*8 = 56 and also 7*2*8 = 112 = 2*56.
%p A073908 f := 7: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);
%Y A073908 Cf. A073906, A085124, A073909, A073910, A073911, A073912.
%K A073908 nonn,base
%O A073908 1,1
%A A073908 _Amarnath Murthy_, Aug 18 2002
%E A073908 More terms from _Sascha Kurz_, Aug 23 2002