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%I #14 Jan 11 2021 23:09:17
%S 2,347,5861,225461,55541,4583,4457,117883,15559,151687,0,155383,0,
%T 5857,118589,126487,0,4789,0,134587,7687,0,0,25867,165457,0,34759,
%U 182687,0,38557,0,44587,0,0,45757,25889,0,0,0,244567,0,148667,0,0,225689,0,0
%N a(n) is the smallest prime 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)=347 because prod(347)=84, sum(347)=14, length(347)=3, n=2 and 84=2*3*14.
%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[k=1, True, k++, m=Prime[k]; If[prod[m]==n*l[m]sum[m], Return[m]]]]
%Y Cf. A007953 (sum), A007954 (prod), A055642 (length), A064022.
%K nonn,base
%O 1,1
%A _Felice Russo_, Sep 18 2001
%E Edited by _Dean Hickerson_, Jun 02 2002