

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
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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



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


CROSSREFS



KEYWORD

nonn,base,easy


AUTHOR



EXTENSIONS



STATUS

approved



