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%I #12 Nov 14 2020 15:52:09
%S 1,10,100,111,1110,11100
%N Divisors of 28 (the 2nd perfect number), written in base 2.
%C The number of divisors of the second perfect number is equal to 2*A000043(2)=A061645(2)=6.
%H <a href="/index/Di#divisors">Index entries for sequences related to divisors of numbers</a>
%F a(n)=A018254(n), written in base 2. Also, for n=1 .. 6: If n<=(A000043(2)=3) then a(n) is the concatenation of the digit "1" and n-1 digits "0" else a(n) is the concatenation of A000043(2)=3 digits "1" and (n-1-A000043(2)) digits "0".
%e The structure of divisors of 28 (see A018254)
%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 .... (The 2nd superperfect number)
%e 4)......... 7 = 2^3 - 2^0 ..... 111 .... (The 2nd Mersenne prime)
%e 5)........ 14 = 2^4 - 2^1 ..... 1110
%e 6)........ 28 = 2^5 - 2^2 ..... 11100... (The 2nd perfect number)
%t FromDigits[IntegerDigits[#,2]]&/@Divisors[28] (* _Harvey P. Dale_, Nov 14 2020 *)
%o (PARI) apply(n->fromdigits(binary(n)), divisors(28)) \\ _Charles R Greathouse IV_, Jun 21 2017
%Y For more information see A018254 (Divisors of 28). 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
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