A355773 Numbers all of whose divisors are members of A333369.

1, 3, 5, 7, 9, 13, 15, 17, 19, 31, 35, 37, 39, 51, 53, 57, 59, 71, 73, 79, 91, 93, 95, 97, 111, 137, 139, 153, 157, 159, 173, 179, 193, 197, 221, 223, 227, 229, 317, 333, 359, 371, 379, 395, 397, 443, 449, 519, 537, 571, 579, 591, 593, 661, 663, 669, 719, 739

Offset: 1

Author

Bernard Schott, Jul 18 2022

Keywords

• nonn
• base

Comments

All terms are necessarily odd because 2 is not in A333369

Examples

			111 is a term since all the divisors of 111, i.e., 1, 3, 37 and 111, are in A333369.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000
• Project Euler, Problem 520: Simbers.

Crossrefs

Cf. A333369, A353735, A355770, A355771, A355772.

Similar sequences: A062687, A190217, A329419, A337741

.

Subsequences: A155045, A355853.

Programs

Mathematica

simQ[n_] := AllTrue[Tally @ IntegerDigits[n], EvenQ[Plus @@ #] &]; Select[Range[1000], AllTrue[Divisors[#], simQ] &] (* Amiram Eldar, Jul 19 2022 *)

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
isok(k) = fordiv(k, d, if (!issimber(d), return(0))); return(1); \\ Michel Marcus, Jul 19 2022

Python

from sympy import divisors, isprime
def c(n): s = str(n); return all(s.count(d)%2 == int(d)%2 for d in set(s))
def ok(n): return n > 0 and all(c(d) for d in divisors(n, generator=True))
print([k for k in range(740) if ok(k)]) # Michael S. Branicky, Jul 24 2022