A182621 a(n) is the concatenation of the binary numbers that are the divisors of n written in base 2.

1, 110, 111, 110100, 1101, 11011110, 1111, 1101001000, 1111001, 1101011010, 11011, 110111001101100, 11101, 1101111110, 1111011111, 110100100010000, 110001, 11011110100110010, 110011, 110100101101010100, 11111110101, 110101110110, 110111, 110111001101000110011000

Offset: 1

Author

Omar E. Pol, Nov 22 2010

Keywords

• nonn
• base
• easy
• less

Comments

a(n) is the concatenation of the numbers of row n of triangle A182620. The first repeated element is a(15) = 1111011111 = a(479), where a(15) is the concatenation of 1, 11, 101 and 1111 but a(479) is the concatenation of 1 and 111011111. See A182620 and A182622 for more information.

Examples

			The divisors of 10 are 1, 2, 5, 10, which written in base 2 are 1, 10, 101, 1010. The concatenation of 1, 10, 101, 1010 is 1101011010, so a(10) = 1101011010.
		

Links

• Jaroslav Krizek, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A007088, A027750, A182620, A182622, A182623, A182624, A182631.

Programs

Mathematica

A182621[n_]:=FromDigits[Flatten[IntegerDigits[Divisors[n],2]]];Array[A182621,50] (* Paolo Xausa, Aug 31 2023 *)

PARI

a(n) = fromdigits(concat(apply(binary,divisors(n)))); \\ Kevin Ryde, May 02 2023

Python

from sympy import divisors
def a(n): return int("".join(bin(d)[2:] for d in divisors(n)))
print([a(n) for n in range(1, 25)]) # Michael S. Branicky, Apr 20 2022

Sage

A182621 = lambda n: Integer(''.join(d.str(base=2) for d in divisors(n))) # D. S. McNeil, Dec 19 2010