A064023 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.

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

Offset

1,1

Comments

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?

Links

Table of n, a(n) for n=1..47.

Example

a(2)=347 because prod(347)=84, sum(347)=14, length(347)=3, n=2 and 84=2*3*14.

Mathematica

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]]]]

Crossrefs

Cf. A007953 (sum), A007954 (prod), A055642 (length), A064022.

Sequence in context: A064501 A063831 A216356 * A370483 A179959 A024350

Adjacent sequences: A064020 A064021 A064022 * A064024 A064025 A064026

Keyword

nonn,base

Author

Felice Russo, Sep 18 2001

Extensions

Edited by Dean Hickerson, Jun 02 2002

Status

approved