A064022 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.

1, 88, 369, 666, 579, 1899, 789, 2688, 999, 3588, 0, 4668, 0, 3789, 4599, 4689, 0, 4789, 0, 5788, 6778, 0, 0, 5889, 35559, 0, 25599, 35667, 0, 35578, 0, 8888, 0, 0, 45577, 25889, 0, 0, 0, 145688, 0, 45579, 0, 0, 55569, 0, 0, 35888, 55677, 245559, 0, 0

Offset

1,2

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..52.

Example

a(2)=88 because prod(88)=64, sum(88)=16, length(88)=2, n=2 and 64=2*2*16.

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[m=1, True, m++, If[prod[m]==n*l[m]sum[m], Return[m]]]]

Crossrefs

Cf. A007953 (sum), A007954 (prod), A055642 (length), A064023.

Sequence in context: A323612 A235019 A241846 * A116065 A234777 A234770

Adjacent sequences: A064019 A064020 A064021 * A064023 A064024 A064025

Keyword

nonn,base

Author

Felice Russo, Sep 18 2001

Extensions

Corrected by Larry Reeves (larryr(AT)acm.org), Sep 20 2001

Edited by Dean Hickerson, Jun 02 2002

Status

approved