A182622 a(n) is the number whose binary representation is the concatenation of the divisors of n written in base 2.

1, 6, 7, 52, 13, 222, 15, 840, 121, 858, 27, 28268, 29, 894, 991, 26896, 49, 113970, 51, 215892, 2037, 3446, 55, 14471576, 441, 3514, 3899, 217052, 61, 14538238, 63, 1721376, 7905, 13410, 7139, 926213284, 101, 13542, 8039, 221009192

Offset

1,2

Comments

a(n) is A182621(n), interpreted as a binary number, written in base 10. The first repeated element is 991, from 15 and 479.

Except for 1, no power of 2 can occur in this sequence, an obvious consequence of the fact that a(n) has to be the sum of at least two distinct powers of 2 for all n > 1. - Alonso del Arte, Nov 13 2013

Links

Indranil Ghosh, Table of n, a(n) for n = 1..50000

Formula

a(p) = 2^(floor(log_2(p)) + 1) + p for p prime. Also, a(p + k) > a(p) for all k > 0. Furthermore, for all primes p > 3, a(p) < a(p - 1).

a(2^(m - 1)) = sum(k = 0 .. m - 1, 2^((m^2 + m)/2 - (k^2 + k)/2 - 1)) = A164894(m). - Alonso del Arte, Nov 13 2013

Example

The divisors of 10 are 1, 2, 5, 10. Then 1, 2, 5, 10 written in base 2 are 1, 10, 101, 1010. The concatenation of 1, 10, 101, 1010 is 1101011010. Then a(10) = 858 because the binary number 1101011010 written in base 10 is 858.

Mathematica

concatBits[n_] := FromDigits[Join @@ (IntegerDigits[#, 2]& /@ Divisors[n]), 2]; concatBits /@ Range[40](* Giovanni Resta, Nov 23 2010 *)

Prog

(Python)
def A182622(n):
....s=""
....for i in range(1, n+1):
........if n%i==0:
............s+=bin(i)[2:]
....return int(s, 2) # Indranil Ghosh, Jan 28 2017
(PARI) a(n) = {my(cbd = []); fordiv(n, d, cbd = concat(cbd, binary(d)); ); fromdigits(cbd, 2); } \\ Michel Marcus, Jan 28 2017

Crossrefs

Cf. A027750, A007088, A182620, A182621, A182623, A182624, A182627, A182632.

Sequence in context: A119108 A248264 A042843 * A028423 A269912 A042117

Adjacent sequences: A182619 A182620 A182621 * A182623 A182624 A182625

Keyword

nonn,base,easy

Author

Omar E. Pol, Nov 22 2010

Extensions

More terms from Giovanni Resta, Nov 23 2010

Status

approved