A135655 - OEIS

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

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OFFSET

1,2

COMMENTS

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).

Index entries for sequences related to divisors of numbers

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.

Sequence in context: A260522 A260521 A136873 * A178500 A178501 A011557

Adjacent sequences: A135652 A135653 A135654 * A135656 A135657 A135658

KEYWORD

base,nonn,fini,full,easy,less

AUTHOR

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

STATUS

approved