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A064023 Smallest prime m such that prod(m)=n*l(m)*sum(m) where prod(m) is the product of the digits of m, l(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. 1

%I

%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 Smallest prime m such that prod(m)=n*l(m)*sum(m) where prod(m) is the product of the digits of m, l(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, l(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. A064022.

%K nonn,base

%O 1,1

%A _Felice Russo_, Sep 18 2001

%E Edited by _Dean Hickerson_, Jun 02 2002

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Last modified June 6 13:49 EDT 2020. Contains 334827 sequences. (Running on oeis4.)