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
KEYWORD
nonn,base,easy
AUTHOR
Omar E. Pol, Nov 22 2010
EXTENSIONS
More terms from Giovanni Resta, Nov 23 2010
STATUS
approved