A135652 Divisors of 28 (the 2nd perfect number), written in base 2.

1, 10, 100, 111, 1110, 11100

Offset

1,2

Comments

The number of divisors of the second perfect number is equal to 2*A000043(2)=A061645(2)=6.

Links

Table of n, a(n) for n=1..6.

Index entries for sequences related to divisors of numbers

Formula

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".

Example

The structure of divisors of 28 (see A018254)
----------------------------------------------------------------------
n ... Divisor . Formula ....... Divisor written in base 2 ............
----------------------------------------------------------------------
1)......... 1 = 2^0 ........... 1
2)......... 2 = 2^1 ........... 10
3)......... 4 = 2^2 ........... 100 .... (The 2nd superperfect number)
4)......... 7 = 2^3 - 2^0 ..... 111 .... (The 2nd Mersenne prime)
5)........ 14 = 2^4 - 2^1 ..... 1110
6)........ 28 = 2^5 - 2^2 ..... 11100... (The 2nd perfect number)

Mathematica

FromDigits[IntegerDigits[#, 2]]&/@Divisors[28] (* Harvey P. Dale, Nov 14 2020 *)

Prog

(PARI) apply(n->fromdigits(binary(n)), divisors(28)) \\ Charles R Greathouse IV, Jun 21 2017

Crossrefs

For more information see A018254 (Divisors of 28). Cf. A000043, A000079, A000396, A000668, A019279, A061645, A061652.

Sequence in context: A273245 A276349 A167502 * A035504 A072366 A349316

Adjacent sequences: A135649 A135650 A135651 * A135653 A135654 A135655

Keyword

base,nonn,fini,full,easy,less

Author

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

Status

approved