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

1, 10, 100, 111, 1110, 11100

Offset: 1

Author

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

Keywords

• base
• nonn
• fini
• full
• easy
• less

Comments

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

Examples

			The structure of divisors of 28 (see A018254)
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n ... Divisor . Formula ....... Divisor written in base 2 ............
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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)
		

Links

• Index entries for sequences related to divisors of numbers

Crossrefs

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

Programs

Mathematica

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

PARI

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

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".