A135653 Divisors of 496 (the 3rd perfect number), written in base 2.

1, 10, 100, 1000, 10000, 11111, 111110, 1111100, 11111000, 111110000

Offset

1,2

Comments

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

Links

Table of n, a(n) for n=1..10.

Index entries for sequences related to divisors of numbers

Formula

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".

Example

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)

Mathematica

FromDigits[IntegerDigits[#, 2]]&/@Divisors[496] (* Harvey P. Dale, Dec 02 2018 *)

Prog

(PARI) apply(n->fromdigits(binary(n)), divisors(496)) \\ Charles R Greathouse IV, Jun 21 2017

Crossrefs

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

Sequence in context: A136866 A136878 A136871 * A219111 A232659 A232660

Adjacent sequences: A135650 A135651 A135652 * A135654 A135655 A135656

Keyword

base,nonn,fini,full,easy,less

Author

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

Status

approved