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).
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 31 2017
STATUS
approved