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

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

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

Examples

			The structure of divisors of 496 (see A018487)
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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 ... (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)
		

Links

• Index entries for sequences related to divisors of numbers

Crossrefs

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

Programs

Mathematica

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

PARI

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

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".