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

1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 1111111111111, 11111111111110, 111111111111100, 1111111111111000, 11111111111110000

Offset: 1

Author

Omar E. Pol, Feb 23 2008, Mar 01 2008, Mar 03 2008

Keywords

• base
• nonn
• fini
• full
• easy
• less

Comments

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

Examples

			The structure of divisors of 33550336 (see A133025)
------------------------------------------------------------------------
n ...... Divisor . Formula ....... Divisor written in base 2 ...........
------------------------------------------------------------------------
1)............ 1 = 2^0 ........... 1
2)............ 2 = 2^1 ........... 10
3)............ 4 = 2^2 ........... 100
4)............ 8 = 2^3 ........... 1000
5)........... 16 = 2^4 ........... 10000
6)........... 32 = 2^5 ........... 100000
7)........... 64 = 2^6 ........... 1000000
8).......... 128 = 2^7 ........... 10000000
9).......... 256 = 2^8 ........... 100000000
10)......... 512 = 2^9 ........... 1000000000
11)........ 1024 = 2^10 .......... 10000000000
12)........ 2048 = 2^11 .......... 100000000000
13) ....... 4096 = 2^12 .......... 1000000000000 ... (The 5th superperfect number)
14) ....... 8191 = 2^13 - 2^0 .... 1111111111111 ... (The 5th Mersenne prime)
15) ...... 16382 = 2^14 - 2^1 .... 11111111111110
16) ...... 32764 = 2^15 - 2^2 .... 111111111111100
17) ...... 65528 = 2^16 - 2^3 .... 1111111111111000
18) ..... 131056 = 2^17 - 2^4 .... 11111111111110000
19) ..... 262112 = 2^18 - 2^5 .... 111111111111100000
20) ..... 524224 = 2^19 - 2^6 .... 1111111111111000000
21) .... 1048448 = 2^20 - 2^7 .... 11111111111110000000
22) .... 2096896 = 2^21 - 2^8 .... 111111111111100000000
23) .... 4193792 = 2^22 - 2^9 .... 1111111111111000000000
24) .... 8387584 = 2^23 - 2^10 ... 11111111111110000000000
25) ... 16775168 = 2^24 - 2^11 ... 111111111111100000000000
26) ... 33550336 = 2^25 - 2^12 ... 1111111111111000000000000 ... (The 5th perfect number)
		

Links

• Omar E. Pol, Table of n, a(n) for n = 1..26 (shows all terms).
• Index entries for sequences related to divisors of numbers

Crossrefs

For more information see A133025 (Divisors of 33550336). Cf. A000043, A000079, A000396, A000668, A019279, A061645, A061652.

Formula

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".