A182621 - OEIS

%I #33 Aug 31 2023 09:51:00

%S 1,110,111,110100,1101,11011110,1111,1101001000,1111001,1101011010,

%T 11011,110111001101100,11101,1101111110,1111011111,110100100010000,

%U 110001,11011110100110010,110011,110100101101010100,11111110101,110101110110,110111,110111001101000110011000

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

%C 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.

%H Jaroslav Krizek, <a href="/A182621/b182621.txt">Table of n, a(n) for n = 1..500</a>

%e 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.

%t A182621[n_]:=FromDigits[Flatten[IntegerDigits[Divisors[n],2]]];Array[A182621,50] (* _Paolo Xausa_, Aug 31 2023 *)

%o (Sage) A182621 = lambda n: Integer(''.join(d.str(base=2) for d in divisors(n))) # _D. S. McNeil_, Dec 19 2010

%o (Python)

%o from sympy import divisors

%o def a(n): return int("".join(bin(d)[2:] for d in divisors(n)))

%o print([a(n) for n in range(1, 25)]) # _Michael S. Branicky_, Apr 20 2022

%o (PARI) a(n) = fromdigits(concat(apply(binary,divisors(n)))); \\ _Kevin Ryde_, May 02 2023

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

%K nonn,base,easy,less

%O 1,2

%A _Omar E. Pol_, Nov 22 2010