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A291022 Even numbers m such that every odd divisor > 1 of m is the sum of two divisors. 0

%I #16 Aug 31 2017 14:17:45

%S 6,12,18,20,24,30,36,40,42,48,54,80,96,100,108,140,150,156,160,162,

%T 192,198,200,220,264,272,280,294,312,320,324,342,384,396,400,440,486,

%U 500,510,520,528,544,546,560,624,640,684,702,714,750,768,798,800,880,912

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

%C 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.

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

%e 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.

%p with(numtheory):EV:=array(1..100):OD:=array(1..100):nn:=5*10^4:

%p for n from 2 by 2 to nn do:

%p d:=divisors(n):n1:=nops(d):k0:=0:k1:=0:it:=0:

%p for i from 1 to n1 do:

%p if irem(d[i],2)=0

%p then

%p k0:=k0+1:EV[k0]:=d[i]:

%p else

%p k1:=k1+1:OD[k1]:=d[i]:

%p fi:

%p od:

%p for j from 2 to k1 do:

%p for k from 1 to k1 do:

%p for l from 1 to k0 do:

%p if OD[j]=OD[k]+EV[l]

%p then

%p it:=it+1:

%p else

%p fi:

%p od:

%p od:

%p od:

%p if it>0 and it = k1-1

%p then

%p printf(`%d, `,n):

%p else

%p fi:

%p od:

%Y Cf. A019434, A088723.

%K nonn

%O 1,1

%A _Michel Lagneau_, Aug 31 2017

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Last modified April 12 16:59 EDT 2024. Contains 371635 sequences. (Running on oeis4.)