A135652 - OEIS

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A135652

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

1, 10, 100, 111, 1110, 11100

(list; graph; refs; listen; history; text; internal format)

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