A342048 Numbers for which the sum of digits equals the product of nonzero digits.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 22, 30, 40, 50, 60, 70, 80, 90, 100, 123, 132, 200, 202, 213, 220, 231, 300, 312, 321, 400, 500, 600, 700, 800, 900, 1000, 1023, 1032, 1124, 1142, 1203, 1214, 1230, 1241, 1302, 1320, 1412, 1421, 2000, 2002, 2013, 2020, 2031, 2103, 2114, 2130, 2141, 2200

Offset: 1

Author

Ilya Gutkovskiy, Feb 26 2021

Keywords

• nonn
• base

Examples

			2103 is in the sequence because 2 + 1 + 0 + 3 = 2 * 1 * 3 = 6.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007953, A034710, A051801.

Programs

Maple

q:= n-> (l-> is(add(i, i=l)=mul(i, i=l)))(
        subs(0=[][], convert(n, base, 10))):
select(q, [$0..3300])[];  # Alois P. Heinz, Feb 26 2021
# alternative
G:= proc(d,dmax,s,p) option remember; local i;
   if s + dmax*d < p or s > dmax^d*p then return [] fi;
   if d = 0 then return [[]] fi;
   [seq(op(map(t -> [i,op(t)], procname(d-1,i,s+i,p*i))),i=1..dmax)]
end proc:
f:= proc(d) local R,k,i;
  R:= [seq(op(map(t -> [0$k,op(t)], G(d-k,9,0,1))),k=0..d-1)];
  R:= map(op@combinat:-permute,R);
  sort(map(t -> add(t[i]*10^(i-1),i=1..d),R))
end proc:
f(4); # Robert Israel, Feb 28 2021

Mathematica

Select[Range[2200], Plus @@ IntegerDigits[#] == Times @@ DeleteCases[IntegerDigits[#], 0] &]

PARI

isok(k) = my(d=select(x->(x>0), digits(k))); vecprod(d) == vecsum(d); \\ Michel Marcus, Feb 26 2021

Python

from math import prod
def ok(n):
  digs = list(map(int, str(n)))
  return sum(digs) == prod([d for d in digs if d != 0])
def aupto(lim): return [m for m in range(1, lim+1) if ok(m)]
print(aupto(2200)) # Michael S. Branicky, Feb 26 2021