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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.

%I A182622 #26 May 22 2025 10:21:35
%S A182622 1,6,7,52,13,222,15,840,121,858,27,28268,29,894,991,26896,49,113970,
%T A182622 51,215892,2037,3446,55,14471576,441,3514,3899,217052,61,14538238,63,
%U A182622 1721376,7905,13410,7139,926213284,101,13542,8039,221009192
%N A182622 a(n) is the number whose binary representation is the concatenation of the divisors of n written in base 2.
%C A182622 a(n) is A182621(n), interpreted as a binary number, written in base 10. The first repeated element is 991, from 15 and 479.
%C A182622 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
%H A182622 Indranil Ghosh, <a href="/A182622/b182622.txt">Table of n, a(n) for n = 1..50000</a>
%F A182622 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).
%F A182622 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
%e A182622 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.
%t A182622 concatBits[n_] := FromDigits[Join @@ (IntegerDigits[#, 2]& /@ Divisors[n]), 2]; concatBits /@ Range[40](* _Giovanni Resta_, Nov 23 2010 *)
%o A182622 (Python)
%o A182622 def A182622(n):
%o A182622     s=""
%o A182622     for i in range(1,n+1):
%o A182622         if n%i==0:
%o A182622             s+=bin(i)[2:]
%o A182622     return int(s,2) # _Indranil Ghosh_, Jan 28 2017
%o A182622 (PARI) a(n) = {my(cbd = []); fordiv(n, d, cbd = concat(cbd, binary(d));); fromdigits(cbd, 2);} \\ _Michel Marcus_, Jan 28 2017
%Y A182622 Cf. A027750, A007088, A182620, A182621, A182623, A182624, A182627, A182632.
%K A182622 nonn,base,easy
%O A182622 1,2
%A A182622 _Omar E. Pol_, Nov 22 2010
%E A182622 More terms from _Giovanni Resta_, Nov 23 2010