A355973 Numbers that can be written as the product of two of its divisors such that the reverse of the binary value of the number equals the concatenation of the binary values of the divisors.

351, 623, 5075, 5535, 21231, 69237, 78205, 88479, 89975, 101239, 173555, 286011, 339183, 357471, 625583, 687245, 1349487, 1415583, 2527343, 3094039, 5426415, 5648031, 5721183, 5764651, 6157723, 8512457, 10137575, 10974951, 11365839, 11775915, 14760911, 18617337, 21587823, 21734127, 22649247

Offset: 1

Author

Scott R. Shannon, Jul 21 2022

Keywords

• nonn
• base

Comments

This is the base-2 equivalent of A009944.

Examples

			351 is a term as 351 = 101011111_2 = 3 * 117 = 11_2 * 1110101_2, and "101011111" in reverse is "111110101" which equals "11" + "1110101".
See the attached text file for other examples.
		

Links

• Scott R. Shannon, Divisor products for the first 46 terms. These are all the terms up to 100000000.

Crossrefs

Cf. A009944, A030190, A210959, A027750.

Programs

Mathematica

Select[Range[2^18], Function[{k, d, m}, AnyTrue[Map[Join @@ IntegerDigits[#, 2] &, Transpose@ {d, k/d}], # == m &]] @@ {#, Divisors[#], Reverse@ IntegerDigits[#, 2]} &] (* Michael De Vlieger, Jul 23 2022 *)

Python

from sympy import divisors
def ok(n):
    if not n&1: return False
    t = bin(n)[2:][::-1]
    return any(t==bin(d)[2:]+bin(n//d)[2:] for d in divisors(n, generator=True))
print([k for k in range(10**6) if ok(k)]) # Michael S. Branicky, Apr 13 2024