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

Author

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

Keywords

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

Comments

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

Examples

			The structure of divisors of 8128 (see A133024)
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n ... Divisor . Formula ....... Divisor written in base 2 ...............
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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)
		

Links

• Index entries for sequences related to divisors of numbers

Crossrefs

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

Programs

Mathematica

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

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".