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 A135655 Divisors of 33550336 (the 5th perfect number), written in base 2. 12

%I

%S 1,10,100,1000,10000,100000,1000000,10000000,100000000,1000000000,

%T 10000000000,100000000000,1000000000000,1111111111111,11111111111110,

%U 111111111111100,1111111111111000,11111111111110000

%N Divisors of 33550336 (the 5th perfect number), written in base 2.

%C The number of divisors of the 5th perfect number is equal to 2*A000043(5)=A061645(5)=26.

%H Omar E. Pol, <a href="/A135655/b135655.txt">Table of n, a(n) for n = 1..26</a> (shows all terms).

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

%F a(n)=A133025(n), written in base 2. Also, for n=1 .. 26: If n<=(A000043(5)=13) then a(n) is the concatenation of the digit "1" and n-1 digits "0" else a(n) is the concatenation of A000043(5)=13 digits "1" and (n-1-A000043(5)) digits "0".

%e The structure of divisors of 33550336 (see A133025)

%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

%e 8).......... 128 = 2^7 ........... 10000000

%e 9).......... 256 = 2^8 ........... 100000000

%e 10)......... 512 = 2^9 ........... 1000000000

%e 11)........ 1024 = 2^10 .......... 10000000000

%e 12)........ 2048 = 2^11 .......... 100000000000

%e 13) ....... 4096 = 2^12 .......... 1000000000000 ... (The 5th superperfect number)

%e 14) ....... 8191 = 2^13 - 2^0 .... 1111111111111 ... (The 5th Mersenne prime)

%e 15) ...... 16382 = 2^14 - 2^1 .... 11111111111110

%e 16) ...... 32764 = 2^15 - 2^2 .... 111111111111100

%e 17) ...... 65528 = 2^16 - 2^3 .... 1111111111111000

%e 18) ..... 131056 = 2^17 - 2^4 .... 11111111111110000

%e 19) ..... 262112 = 2^18 - 2^5 .... 111111111111100000

%e 20) ..... 524224 = 2^19 - 2^6 .... 1111111111111000000

%e 21) .... 1048448 = 2^20 - 2^7 .... 11111111111110000000

%e 22) .... 2096896 = 2^21 - 2^8 .... 111111111111100000000

%e 23) .... 4193792 = 2^22 - 2^9 .... 1111111111111000000000

%e 24) .... 8387584 = 2^23 - 2^10 ... 11111111111110000000000

%e 25) ... 16775168 = 2^24 - 2^11 ... 111111111111100000000000

%e 26) ... 33550336 = 2^25 - 2^12 ... 1111111111111000000000000 ... (The 5th perfect number)

%Y For more information see A133025 (Divisors of 33550336). 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 01 2008, Mar 03 2008

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