A204879 Numbers that can be written as sum of perfect numbers.

6, 12, 18, 24, 28, 30, 34, 36, 40, 42, 46, 48, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130, 132, 134, 136, 138, 140, 142, 144

Offset

1,1

Comments

Complement of A204878; A097796(a(n)) > 0.

Up to the first odd perfect number (known to be > 10^300, if it exists), also: positive integers of the form 6k+28m, k>=0, m>=0. Contains all even numbers > 50, since any such number is either of the form 6k or 6k+28 or 6k+28*2. - M. F. Hasler, Feb 09 2012

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Eric Weisstein's World of Mathematics, Perfect Number

Wikipedia, Perfect number

Formula

A204879 = { 2k; k>25 } union { 6k; k>0 } union { 28, 34, 40, 46 }

Prog

(Haskell)
import Data.List (findIndices)
a204879 n = a204879_list !! (n-1)
a204879_list = map (+ 1) $ findIndices (> 0) a097796_list
(PARI) (Contribution from M. F. Hasler, Feb 09 2012) (Start)
/* The following code is valid up to occurrence of the first odd perfect number (if it exists), thus at least up to 10^300 */
is_A204879(n)={ n%2&return; n>50 || n%6==0 || n==28 || n==34 || n==40 || n==46 }
A204879(n)={ if(n>12, n+13, 3*n-if(n>4, n*3\2-6))*2 }  \\ (End)

Crossrefs

Cf. A000396 (perfect numbers).

Sequence in context: A037917 A336339 A282146 * A326696 A097603 A362801

Adjacent sequences: A204876 A204877 A204878 * A204880 A204881 A204882

Keyword

nonn

Author

Reinhard Zumkeller, Jan 20 2012

Status

approved