1,2

The number of divisors of the third perfect number is equal to 2*A000043(3)=A061645(3)=10.

a(n)=A018487(n), written in base 2. Also, for n=1 .. 10: If n<=(A000043(3)=5) then a(n) is the concatenation of the digit "1" and n-1 digits "0" else a(n) is the concatenation of A000043(3)=5 digits "1" and (n-1-A000043(3)) digits "0".

The structure of divisors of 496 (See A018487)

-------------------------------------------------------------------------

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 ... (The 3rd superperfect number)

6)........ 31 = 2^5 - 2^0 ..... 11111 ... (The 3rd Mersenne prime)

7)........ 62 = 2^6 - 2^1 ..... 111110

8)....... 124 = 2^7 - 2^2 ..... 1111100

9)....... 248 = 2^8 - 2^3 ..... 11111000

10)...... 496 = 2^9 - 2^4 ..... 111110000 ... (The 3rd perfect number)

For more information see A018487 (Divisors of 496). Cf. A000043, A000079, A000396, A000668, A019279, A061645, A061652.

Sequence in context: A136866 A136878 A136871 this_sequence A052211 A136845 A136837

Adjacent sequences: A135650 A135651 A135652 this_sequence A135654 A135655 A135656

base,nonn,fini,full

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