A291022 Even numbers m such that every odd divisor > 1 of m is the sum of two divisors.

6, 12, 18, 20, 24, 30, 36, 40, 42, 48, 54, 80, 96, 100, 108, 140, 150, 156, 160, 162, 192, 198, 200, 220, 264, 272, 280, 294, 312, 320, 324, 342, 384, 396, 400, 440, 486, 500, 510, 520, 528, 544, 546, 560, 624, 640, 684, 702, 714, 750, 768, 798, 800, 880, 912

Offset

1,1

Comments

The numbers of the form p*2^q (6, 12, 20, ...) where p belongs to the set {3, 5, 17, 257, 65537} (A019434: Fermat primes or primes of the form 2^(2^k) + 1, for some k >= 0) are in the sequence.

The sequence is included in A088723 (Numbers having at least one divisor d>1 such that also d+1 is a divisor).

Links

Table of n, a(n) for n=1..55.

Example

42 is in the sequence because the divisors are {1, 2, 3, 6, 7, 14, 21, 42} and 3 = 2 + 1, 7 = 6 + 1 and 21 = 14 + 7.

Maple

with(numtheory):EV:=array(1..100):OD:=array(1..100):nn:=5*10^4:
for n from 2 by 2 to nn do:
  d:=divisors(n):n1:=nops(d):k0:=0:k1:=0:it:=0:
   for i from 1 to n1 do:
    if irem(d[i], 2)=0
     then
     k0:=k0+1:EV[k0]:=d[i]:
     else
     k1:=k1+1:OD[k1]:=d[i]:
    fi:
   od:
     for j from 2 to k1 do:
       for k from 1 to k1 do:
         for l from 1 to k0 do:
          if OD[j]=OD[k]+EV[l]
         then
          it:=it+1:
          else
         fi:
       od:
      od:
     od:
     if it>0 and it = k1-1
      then
      printf(`%d, `, n):
      else
     fi:
  od:

Crossrefs

Cf. A019434, A088723.

Sequence in context: A094519 A088723 A228870 * A348719 A316221 A138939

Adjacent sequences: A291019 A291020 A291021 * A291023 A291024 A291025

Keyword

nonn

Author

Michel Lagneau, Aug 31 2017

Status

approved