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

1,2

Comments

Multiplicative closure of A036953.

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Supersequence of A036953. Cf. A385345.

Sequence in context: A115797 A336627 A242313 * A003596 A018600 A018408

Adjacent sequences: A385341 A385342 A385343 * A385345 A385346 A385347

Keyword

nonn,base,easy

Author

Jens Ahlström, Jun 26 2025

Status

approved