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A346217 Integers m, with k digits, such that Sum_{i=1..k} (m without its i-th digit)/(its i-th digit) is an integer.

%I A346217 #17 Aug 05 2021 16:28:11
%S A346217 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,122,124,126,142,144,
%T A346217 155,162,168,186,221,222,244,248,261,263,284,288,324,326,333,342,346,
%U A346217 362,364,366,442,444,488,555,621,623,648,663,666,684,728,742,777,812
%N A346217 Integers m, with k digits, such that Sum_{i=1..k} (m without its i-th digit)/(its i-th digit) is an integer.
%H A346217 Michel Marcus, <a href="/A346217/b346217.txt">Table of n, a(n) for n = 1..5000</a>
%H A346217 Carlos Rivera, <a href="http://www.primepuzzles.net/puzzles/puzz_1045.htm">Puzzle 1045. One nice puzzle from Paolo Lava</a>, The Prime Puzzles and Problems Connection.
%e A346217 124 gives 12/4 + 14/2 + 24/1 = 34, an integer, so 124 is a term.
%e A346217 221 gives 21/2 + 21/2 + 22/1 = 43, an integer, so 221 is a term.
%o A346217 (PARI) subs(d, j) = {my(x=""); for (k=1, #d, if (j != k, x = concat(x, d[k]));); eval(x);}
%o A346217 isok(m) = {my(d=digits(m), res); if (vecmin(d), res = sum(j=1, #d, subs(d, j)/d[j]); (denominator(res)==1););}
%o A346217 (Python)
%o A346217 from fractions import Fraction
%o A346217 def ok(n):
%o A346217     s = str(n)
%o A346217     if '0' in s: return False
%o A346217     if len(s) == 1: return True
%o A346217     return sum(Fraction(int(s[:i]+s[i+1:]), int(s[i])) for i in range(len(s))).denominator == 1
%o A346217 print(list(filter(ok, range(813)))) # _Michael S. Branicky_, Jul 11 2021
%Y A346217 Subsequence of A052382 (zeroless numbers). Supersequence of A346206.
%K A346217 nonn,base
%O A346217 1,2
%A A346217 _Michel Marcus_, Jul 11 2021