A385344 Numbers where all the digits of all the prime factors are smaller than 3.

1, 2, 4, 8, 11, 16, 22, 32, 44, 64, 88, 101, 121, 128, 176, 202, 211, 242, 256, 352, 404, 422, 484, 512, 704, 808, 844, 968, 1021, 1024, 1111, 1201, 1331, 1408, 1616, 1688, 1936, 2011, 2042, 2048, 2111, 2221, 2222, 2321, 2402, 2662, 2816, 3232, 3376, 3872, 4022, 4084, 4096, 4222, 4442, 4444, 4642, 4804, 5324, 5632

Offset: 1

Author

Jens Ahlström, Jun 26 2025

Keywords

• nonn
• base
• easy

Comments

Multiplicative closure of A036953.

Examples

			202 is in the sequence since the prime factors 2 and 101 both have all digits smaller than 3.
34 is not in the sequence since it has the prime factor 17 that have a digit larger than 2.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000

Crossrefs

Supersequence of A036953. Cf. A385345.

Programs

Mathematica

A385344Q[k_] := AllTrue[FactorInteger[k][[All, 1]], Max[IntegerDigits[#]] < 3 &];
Select[Range[10000], A385344Q] (* Paolo Xausa, Jun 28 2025 *)

Python

from sympy import primefactors
def ok(n): return all(set(str(f)) <= set("012") for f in primefactors(n))
print([k for k in range(1, 6000) if ok(k)]) # Michael S. Branicky, Jun 26 2025

Formula

{k | all prime factors of k are in A036953}. - Michael S. Branicky, Jun 26 2025