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A291022 Even numbers m such that every odd divisor > 1 of m is the sum of two divisors. 0
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 (list; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A094519 A088723 A228870 * A348719 A316221 A138939
KEYWORD
nonn
AUTHOR
Michel Lagneau, Aug 31 2017
STATUS
approved

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Last modified February 28 21:38 EST 2024. Contains 370400 sequences. (Running on oeis4.)