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A182622 a(n) is the number whose binary representation is the concatenation of the divisors of n written in base 2. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 26 13:17 EDT 2022. Contains 354092 sequences. (Running on oeis4.)