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%I #12 Jan 22 2021 13:57:40
%S 1,2,12,112,220,222,2212,32,12222,1230,1232,2232,22230,1330,30030,
%T 3232,20332,1000332,223231,33300,23331,132330,213233,233232,12233300,
%U 104,12222333,224,2204,12240,341,3040,202224,10234,23240,2000304,3034,4332,30342,133240,220334,1032234
%N Smallest multiple of n whose factorial digit sum equals n.
%e a(7) = 2212 = 7*316 because 2! + 2! + 1! + 2! = 7.
%p with(numtheory): for n from 1 to 42 do: found:=false: for k from n by n while not found do q:=k: s:=0:
%p for m from 1 to length(k) do s:=s+irem(q, 10)! : q:=iquo(q, 10): od:
%p if s=n then found:=true: printf(`%d, `, k) fi od od:
%t smn[n_]:=Module[{m=1},While[Total[IntegerDigits[m*n]!]!=n,m++];m*n]; Array[ smn,50] (* _Harvey P. Dale_, Nov 17 2018 *)
%o (PARI) a(n)={ my(t,d=49); while((d-47)!<=n,d++); forstep(k=n,9e99,n, t=Vecsmall(Str(k)); if( t[1]>d, k=(10^#t-1)\n*n, sum(j=1,#t,(t[j]-48)!)==n&return(k)))} \\ _M. F. Hasler_, Jun 20 2011
%K nonn,base
%O 1,2
%A _Michel Lagneau_, Jun 18 2011
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