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A064023
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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.
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1
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2, 347, 5861, 225461, 55541, 4583, 4457, 117883, 15559, 151687, 0, 155383, 0, 5857, 118589, 126487, 0, 4789, 0, 134587, 7687, 0, 0, 25867, 165457, 0, 34759, 182687, 0, 38557, 0, 44587, 0, 0, 45757, 25889, 0, 0, 0, 244567, 0, 148667, 0, 0, 225689, 0, 0
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OFFSET
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1,1
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COMMENTS
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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?
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LINKS
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EXAMPLE
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a(2)=347 because prod(347)=84, sum(347)=14, length(347)=3, n=2 and 84=2*3*14.
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MATHEMATICA
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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]]]]
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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