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

1,2

Comments

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

Links

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

Formula

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Supersequence of A020449.

Cf. A385344.

Sequence in context: A303570 A208262 A062696 * A113654 A066592 A316604

Adjacent sequences: A385342 A385343 A385344 * A385346 A385347 A385348

Keyword

nonn,base

Author

Jens Ahlström, Jun 26 2025

Status

approved