cp's OEIS Frontend

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

%I A135653 #12 Dec 02 2018 18:54:29
%S A135653 1,10,100,1000,10000,11111,111110,1111100,11111000,111110000
%N A135653 Divisors of 496 (the 3rd perfect number), written in base 2.
%C A135653 The number of divisors of the third perfect number is equal to 2*A000043(3)=A061645(3)=10.
%H A135653 <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%F A135653 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 A135653 The structure of divisors of 496 (see A018487)
%e A135653 -------------------------------------------------------------------------
%e A135653 n ... Divisor . Formula ....... Divisor written in base 2 ...............
%e A135653 -------------------------------------------------------------------------
%e A135653 1)......... 1 = 2^0 ........... 1
%e A135653 2)......... 2 = 2^1 ........... 10
%e A135653 3)......... 4 = 2^2 ........... 100
%e A135653 4)......... 8 = 2^3 ........... 1000
%e A135653 5)........ 16 = 2^4 ........... 10000 ... (The 3rd superperfect number)
%e A135653 6)........ 31 = 2^5 - 2^0 ..... 11111 ... (The 3rd Mersenne prime)
%e A135653 7)........ 62 = 2^6 - 2^1 ..... 111110
%e A135653 8)....... 124 = 2^7 - 2^2 ..... 1111100
%e A135653 9)....... 248 = 2^8 - 2^3 ..... 11111000
%e A135653 10)...... 496 = 2^9 - 2^4 ..... 111110000 ... (The 3rd perfect number)
%t A135653 FromDigits[IntegerDigits[#,2]]&/@Divisors[496] (* _Harvey P. Dale_, Dec 02 2018 *)
%o A135653 (PARI) apply(n->fromdigits(binary(n)), divisors(496)) \\ _Charles R Greathouse IV_, Jun 21 2017
%Y A135653 For more information see A018487 (Divisors of 496). Cf. A000043, A000079, A000396, A000668, A019279, A061645, A061652.
%K A135653 base,nonn,fini,full,easy,less
%O A135653 1,2
%A A135653 _Omar E. Pol_, Feb 23 2008, Mar 03 2008