

A126789


a(n) is the smallest number such that the product of its digits is n times the sum of its digits, or 0 if no such number exists.


2



1, 36, 66, 88, 257, 268, 279, 448, 369, 459, 0, 666, 0, 578, 579, 678, 0, 1689, 0, 2558, 789, 0, 0, 1899, 13557, 0, 999, 3477, 0, 2589, 0, 2688, 0, 0, 13578, 3489, 0, 0, 0, 3588, 0, 2799, 0, 0, 4569, 0, 0, 4668, 4677, 5568, 0, 0, 0, 3699, 0, 3789, 0, 0, 0, 4599, 0, 0
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OFFSET

1,2


COMMENTS

a(11) = 0. Proof: 11 is a prime number and the product of digits of a number in base 10 can never be a multiple of 11.  Stefan Steinerberger, Jun 07 2007
More generally, a(n) = 0 for all n which are divisible by a prime bigger than 7. This means that the sequence will almost always be 0 (with the set of exceptions having density 0). In each term the digits will be increasing (otherwise we could rearrange the digits so that they form a smaller number with the specified property). If no prime factors of n exceed 7, does this mean that a(n) is not 0?  Stefan Steinerberger, Jun 14 2007


LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..10000


EXAMPLE

a(2)=36 because 3*6/(3+6) = 2 and no number smaller than 36 has this property.


MAPLE

for n from 1 to 10 do b:=proc(k) local kk: kk:=convert(k, base, 10): if product(kk[j], j=1..nops(kk))=n*sum(kk[j], j=1..nops(kk)) then k else fi end: a[n]:=[seq(b(k), k=1..1000)][1]: od: seq(a[n], n=1..10); # program works only for n from 1 to 10 Emeric Deutsch, Mar 07 2007


MATHEMATICA

a[1] := 1; a[n_] := Module[{}, k = 0; If[FactorInteger[n][[ 1, 1]] < 8, k = 1; While[Times @@ IntegerDigits[k] != n*Plus @@ IntegerDigits[k], k++ ]]; k]; Table[a[i], {i, 1, 80}] (* Stefan Steinerberger, Jun 14 2007 *)


CROSSREFS

This sequence is a subsequence of A061013 (Product of digits of n) is divisible by (sum of digits of n), where 0's are not permitted.
Sequence in context: A269499 A074315 A240520 * A176623 A211724 A250771
Adjacent sequences: A126786 A126787 A126788 * A126790 A126791 A126792


KEYWORD

base,nonn


AUTHOR

Tanya Khovanova, Feb 19 2007


EXTENSIONS

More terms from Emeric Deutsch, Mar 07 2007
More terms from Stefan Steinerberger, Jun 14 2007


STATUS

approved



