A135653 - OEIS

%I #12 Dec 02 2018 18:54:29

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

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

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

%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>

%F 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".

%e The structure of divisors of 496 (see A018487)

%e -------------------------------------------------------------------------

%e n ... Divisor . Formula ....... Divisor written in base 2 ...............

%e -------------------------------------------------------------------------

%e 1)......... 1 = 2^0 ........... 1

%e 2)......... 2 = 2^1 ........... 10

%e 3)......... 4 = 2^2 ........... 100

%e 4)......... 8 = 2^3 ........... 1000

%e 5)........ 16 = 2^4 ........... 10000 ... (The 3rd superperfect number)

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

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

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

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

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

%t FromDigits[IntegerDigits[#,2]]&/@Divisors[496] (* _Harvey P. Dale_, Dec 02 2018 *)

%o (PARI) apply(n->fromdigits(binary(n)), divisors(496)) \\ _Charles R Greathouse IV_, Jun 21 2017

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

%K base,nonn,fini,full,easy,less

%O 1,2

%A _Omar E. Pol_, Feb 23 2008, Mar 03 2008