A385345 Numbers without a prime factor with a digit larger than 1.

1, 11, 101, 121, 1111, 1331, 10111, 10201, 12221, 14641, 101111, 111221, 112211, 134431, 161051, 1011001, 1021211, 1030301, 1100101, 1112221, 1223431, 1234321, 1478741, 1771561, 10010101, 10011101, 10100011, 10101101, 10110011, 10111001, 10212211, 11000111, 11100101, 11110111, 11111101

Offset: 1

Author

Jens Ahlström, Jun 26 2025

Keywords

• nonn
• base

Comments

Numbers where all the digits of the prime factors are either 1 or 0. Multiplicative closure of A020449.

Examples

			121 = 11 * 11 is in the sequence, since its only prime factor 11 does not have any digits larger than 1.
1001 = 7 * 13 * 11 is not in the sequence since 7 and 13 has digits larger than 1.
		

Links

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

Crossrefs

Supersequence of A020449.

Cf. A385344.

Programs

Mathematica

Select[Range[2*10^6],AllTrue[IntegerDigits/@First/@FactorInteger[#]//Flatten,#<2&]&] (* James C. McMahon, Jun 28 2025 *)

Python

from sympy import primefactors
def ok(n): return all(set(str(p)) <= set("01") for p in primefactors(n))
print([k for k in range(1, 2*10**6) if ok(k)]) # Michael S. Branicky, Jun 26 2025

Formula

{k | all prime factors of k are in A020449}. - Michael S. Branicky, Jun 26 2025