A191895 Smallest multiple of n whose factorial digit sum equals n.

1, 2, 12, 112, 220, 222, 2212, 32, 12222, 1230, 1232, 2232, 22230, 1330, 30030, 3232, 20332, 1000332, 223231, 33300, 23331, 132330, 213233, 233232, 12233300, 104, 12222333, 224, 2204, 12240, 341, 3040, 202224, 10234, 23240, 2000304, 3034, 4332, 30342, 133240, 220334, 1032234

Offset

1,2

Links

Table of n, a(n) for n=1..42.

Example

a(7) = 2212 = 7*316 because 2! + 2! + 1! + 2! = 7.

Maple

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:
for m from 1 to length(k) do s:=s+irem(q, 10)! : q:=iquo(q, 10): od:
if s=n then found:=true: printf(`%d, `, k) fi od od:

Mathematica

smn[n_]:=Module[{m=1}, While[Total[IntegerDigits[m*n]!]!=n, m++]; m*n]; Array[ smn, 50] (* Harvey P. Dale, Nov 17 2018 *)

Prog

(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

Crossrefs

Sequence in context: A207778 A102659 A212659 * A047855 A199045 A009232

Adjacent sequences: A191892 A191893 A191894 * A191896 A191897 A191898

Keyword

nonn,base

Author

Michel Lagneau, Jun 18 2011

Status

approved