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A135655 Divisors of 33550336 (the 5th perfect number), written in base 2. +0
12
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 1111111111111, 11111111111110, 111111111111100, 1111111111111000, 11111111111110000 (list; graph; listen)
OFFSET

1,2

COMMENT

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

LINKS

Omar E. Pol, Table of n, a(n) for n = 1..26 [Shows all terms]

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".

EXAMPLE

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)

CROSSREFS

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

Adjacent sequences: A135652 A135653 A135654 this_sequence A135656 A135657 A135658

Sequence in context: A125858 A086067 A136873 this_sequence A011557 A138825 A138824

KEYWORD

base,nonn,fini

AUTHOR

Omar E. Pol (info(AT)polprimos.com), Feb 23 2008, Mar 01 2008, Mar 03 2008

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Last modified October 6 16:13 EDT 2008. Contains 144667 sequences.


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