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A355773 Numbers all of whose divisors are members of A333369.

%I A355773 #39 Sep 04 2022 13:01:18
%S A355773 1,3,5,7,9,13,15,17,19,31,35,37,39,51,53,57,59,71,73,79,91,93,95,97,
%T A355773 111,137,139,153,157,159,173,179,193,197,221,223,227,229,317,333,359,
%U A355773 371,379,395,397,443,449,519,537,571,579,591,593,661,663,669,719,739
%N A355773 Numbers all of whose divisors are members of A333369.
%C A355773 All terms are necessarily odd because 2 is not in A333369
%H A355773 Michael S. Branicky, <a href="/A355773/b355773.txt">Table of n, a(n) for n = 1..10000</a>
%H A355773 Project Euler, <a href="https://projecteuler.net/problem=520">Problem 520: Simbers</a>.
%e A355773 111 is a term since all the divisors of 111, i.e., 1, 3, 37 and 111, are in A333369.
%t A355773 simQ[n_] := AllTrue[Tally @ IntegerDigits[n], EvenQ[Plus @@ #] &]; Select[Range[1000], AllTrue[Divisors[#], simQ] &] (* _Amiram Eldar_, Jul 19 2022 *)
%o A355773 (PARI) issimber(m) = my(d=digits(m), s=Set(d)); for (i=1, #s, if (#select(x->(x==s[i]), d) % 2 != (s[i] % 2), return (0))); return (1); \\ A333369
%o A355773 isok(k) = fordiv(k, d, if (!issimber(d), return(0))); return(1); \\ _Michel Marcus_, Jul 19 2022
%o A355773 (Python)
%o A355773 from sympy import divisors, isprime
%o A355773 def c(n): s = str(n); return all(s.count(d)%2 == int(d)%2 for d in set(s))
%o A355773 def ok(n): return n > 0 and all(c(d) for d in divisors(n, generator=True))
%o A355773 print([k for k in range(740) if ok(k)]) # _Michael S. Branicky_, Jul 24 2022
%Y A355773 Cf. A333369, A353735, A355770, A355771, A355772.
%Y A355773 Similar sequences: A062687, A190217, A329419, A337741
%Y A355773 .
%Y A355773 Subsequences: A155045, A355853.
%K A355773 nonn,base
%O A355773 1,2
%A A355773 _Bernard Schott_, Jul 18 2022