A355791 Numbers that can be written as the product of two divisors greater than 1 such that the number in binary is contained in the string concatenation of the divisors in binary.

6, 10, 12, 14, 24, 28, 30, 36, 42, 48, 56, 57, 60, 62, 96, 112, 120, 124, 126, 136, 170, 192, 224, 240, 248, 252, 254, 292, 355, 384, 448, 480, 496, 504, 508, 510, 528, 682, 737, 768, 896, 921, 960, 992, 1008, 1016, 1020, 1022, 1536, 1792, 1920, 1984, 2016, 2032, 2040, 2044, 2046, 2080, 2184, 2340

Offset: 1

Author

Scott R. Shannon, Jul 17 2022

Keywords

• nonn
• base

Examples

			6 is a term as 6 = 110_2 = 3 * 2 = 11_2 * 10_2 and "11" + "10" = "1110" contains "110".
2340 is a term as 2340 = 100100100100_2 = 4 * 585 = 100_2 * 1001001001_2 and "100" + "1001001001" contains "100100100100".
See the attached text file for other examples.
		

Links

• Scott R. Shannon, Divisor product of the first 417 terms. These are all the numbers up to 100000000.

Crossrefs

Cf. A355790 (base-10), A355852, A355857, A030190, A355852, A210959, A027750.

Programs

Mathematica

q[n_] := AnyTrue[Rest @ Most @ Divisors[n], StringContainsQ[StringJoin @@ IntegerString[{#, n/#}, 2], IntegerString[n, 2]] &]; Select[Range[2, 2500], q] (* Amiram Eldar, Jul 27 2022 *)

Python

from sympy import divisors
def ok(n):
    b, divs = bin(n)[2:], divisors(n)[1:-1]
    return any(b in bin(d)[2:]+bin(n//d)[2:] for d in divs)
print([k for k in range(1, 2400) if ok(k)]) # Michael S. Branicky, Jul 27 2022