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A135655 Divisors of 33550336 (the 5th perfect number), written in base 2. 13
1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, 100000000000, 1000000000000, 1111111111111, 11111111111110, 111111111111100, 1111111111111000, 11111111111110000 (list; graph; refs; listen; history; text; internal format)
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).
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
KEYWORD
base,nonn,fini,full,easy,less
AUTHOR
Omar E. Pol, Feb 23 2008, Mar 01 2008, Mar 03 2008
STATUS
approved

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Last modified March 19 03:21 EDT 2024. Contains 370952 sequences. (Running on oeis4.)