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%I #16 Jan 10 2021 11:01:32
%S 1,88,369,666,579,1899,789,2688,999,3588,0,4668,0,3789,4599,4689,0,
%T 4789,0,5788,6778,0,0,5889,35559,0,25599,35667,0,35578,0,8888,0,0,
%U 45577,25889,0,0,0,145688,0,45579,0,0,55569,0,0,35888,55677,245559,0,0
%N a(n) is the smallest value of m such that prod(m) = n*length(m)*sum(m) where prod(m) is the product of the digits of m, length(m) is the number of digits of m, sum(m) is the sum of the digits of m; or 0 if no such m exists.
%C If n is divisible by a prime larger than 7, then n can't divide prod(m), so a(n)=0. Are there any other values of n with a(n)=0?
%e a(2)=88 because prod(88)=64, sum(88)=16, length(88)=2, n=2 and 64=2*2*16.
%t id := IntegerDigits; prod[n_] := Times@@id[n]; l[n_] := Length[id[n]]; sum[n_] := Plus@@id[n]; a[n_] := If[FactorInteger[2n][[ -1, 1]]>7, 0, For[m=1, True, m++, If[prod[m]==n*l[m]sum[m], Return[m]]]]
%Y Cf. A007953 (sum), A007954 (prod), A055642 (length), A064023.
%K nonn,base
%O 1,2
%A _Felice Russo_, Sep 18 2001
%E Corrected by Larry Reeves (larryr(AT)acm.org), Sep 20 2001
%E Edited by _Dean Hickerson_, Jun 02 2002
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