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

1,1

Comments

This is the base-2 equivalent of A009944.

Links

Table of n, a(n) for n=1..35.

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A009944, A030190, A210959, A027750.

Sequence in context: A281555 A363422 A267939 * A092374 A273255 A264426

Adjacent sequences: A355970 A355971 A355972 * A355974 A355975 A355976

Keyword

nonn,base

Author

Scott R. Shannon, Jul 21 2022

Status

approved