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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.
2
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
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
KEYWORD
nonn,base
AUTHOR
Scott R. Shannon, Jul 21 2022
STATUS
approved