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

Author

Reinhard Zumkeller, Jan 20 2012

Keywords

• nonn

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

Crossrefs

Cf. A000396 (perfect numbers).

Programs

Haskell

import Data.List (findIndices)
a204879 n = a204879_list !! (n-1)
a204879_list = map (+ 1) $ findIndices (> 0) a097796_list

PARI

/* 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 } \\ M. F. Hasler, Feb 09 2012

Formula

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