%I #10 Jan 08 2014 16:12:41

%S 1,10,100,1000,10000,100000,1000000,1111111,11111110,111111100,

%T 1111111000,11111110000,111111100000,1111111000000

%N Divisors of 8128 (the 4th perfect number), written in base 2.

%C The number of divisors of the 4th perfect number is equal to 2*A000043(4)=A061645(4)=14.

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%F a(n)=A133024(n), written in base 2. Also, for n=1 .. 14: If n<=(A000043(4)=7) then a(n) is the concatenation of the digit "1" and n-1 digits "0" else a(n) is the concatenation of A000043(4)=7 digits "1" and (n-1-A000043(4)) digits "0".

%e The structure of divisors of 8128 (see A133024)

%e -------------------------------------------------------------------------

%e n ... Divisor . Formula ....... Divisor written in base 2 ...............

%e -------------------------------------------------------------------------

%e 1)......... 1 = 2^0 ........... 1

%e 2)......... 2 = 2^1 ........... 10

%e 3)......... 4 = 2^2 ........... 100

%e 4)......... 8 = 2^3 ........... 1000

%e 5)........ 16 = 2^4 ........... 10000

%e 6)........ 32 = 2^5 ........... 100000

%e 7)........ 64 = 2^6 ........... 1000000 ... (The 4th superperfect number)

%e 8)....... 127 = 2^7 - 2^0 ..... 1111111 ... (The 4th Mersenne prime)

%e 9)....... 254 = 2^8 - 2^1 ..... 11111110

%e 10)...... 508 = 2^9 - 2^2 ..... 111111100

%e 11)..... 1016 = 2^10- 2^3 ..... 1111111000

%e 12)..... 2032 = 2^11- 2^4 ..... 11111110000

%e 13)..... 4064 = 2^12- 2^5 ..... 111111100000

%e 14)..... 8128 = 2^13- 2^6 ..... 1111111000000 ... (The 4th perfect number)

%t FromDigits[IntegerDigits[#,2]]&/@Divisors[8128] (* _Harvey P. Dale_, Jan 08 2014 *)

%Y For more information see A133024 (Divisors of 8128). Cf. A000043, A000079, A000396, A000668, A019279, A061645, A061652.

%K base,nonn,fini,full,easy,less

%O 1,2

%A _Omar E. Pol_, Feb 23 2008, Mar 03 2008