A135654 Divisors of 8128 (the 4th perfect number), written in base 2.

1, 10, 100, 1000, 10000, 100000, 1000000, 1111111, 11111110, 111111100, 1111111000, 11111110000, 111111100000, 1111111000000

Offset

1,2

Comments

The number of divisors of the 4th perfect number is equal to 2*A000043(4)=A061645(4)=14.

Links

Table of n, a(n) for n=1..14.

Index entries for sequences related to divisors of numbers

Formula

a(n)=A133024(n), written in base 2. Also, for n=1 .. 14: If n<=(A000043(4)=7) then a(n) is the concatenation of the digit "1" and n-1 digits "0" else a(n) is the concatenation of A000043(4)=7 digits "1" and (n-1-A000043(4)) digits "0".

Example

The structure of divisors of 8128 (see A133024)
-------------------------------------------------------------------------
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 ... (The 4th superperfect number)
8)....... 127 = 2^7 - 2^0 ..... 1111111 ... (The 4th Mersenne prime)
9)....... 254 = 2^8 - 2^1 ..... 11111110
10)...... 508 = 2^9 - 2^2 ..... 111111100
11)..... 1016 = 2^10- 2^3 ..... 1111111000
12)..... 2032 = 2^11- 2^4 ..... 11111110000
13)..... 4064 = 2^12- 2^5 ..... 111111100000
14)..... 8128 = 2^13- 2^6 ..... 1111111000000 ... (The 4th perfect number)

Mathematica

FromDigits[IntegerDigits[#, 2]]&/@Divisors[8128] (* Harvey P. Dale, Jan 08 2014 *)

Crossrefs

For more information see A133024 (Divisors of 8128). Cf. A000043, A000079, A000396, A000668, A019279, A061645, A061652.

Sequence in context: A136872 A119084 A136875 * A219112 A232661 A029800

Adjacent sequences: A135651 A135652 A135653 * A135655 A135656 A135657

Keyword

base,nonn,fini,full,easy,less

Author

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

Status

approved