cp's OEIS Frontend

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

%I A291022 #16 Aug 31 2017 14:17:45
%S A291022 6,12,18,20,24,30,36,40,42,48,54,80,96,100,108,140,150,156,160,162,
%T A291022 192,198,200,220,264,272,280,294,312,320,324,342,384,396,400,440,486,
%U A291022 500,510,520,528,544,546,560,624,640,684,702,714,750,768,798,800,880,912
%N A291022 Even numbers m such that every odd divisor > 1 of m is the sum of two divisors.
%C A291022 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 A291022 The sequence is included in A088723 (Numbers having at least one divisor d>1 such that also d+1 is a divisor).
%e A291022 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 A291022 with(numtheory):EV:=array(1..100):OD:=array(1..100):nn:=5*10^4:
%p A291022 for n from 2 by 2 to nn do:
%p A291022   d:=divisors(n):n1:=nops(d):k0:=0:k1:=0:it:=0:
%p A291022    for i from 1 to n1 do:
%p A291022     if irem(d[i],2)=0
%p A291022      then
%p A291022      k0:=k0+1:EV[k0]:=d[i]:
%p A291022      else
%p A291022      k1:=k1+1:OD[k1]:=d[i]:
%p A291022     fi:
%p A291022    od:
%p A291022      for j from 2 to k1 do:
%p A291022        for k from 1 to k1 do:
%p A291022          for l from 1 to k0 do:
%p A291022           if OD[j]=OD[k]+EV[l]
%p A291022          then
%p A291022           it:=it+1:
%p A291022           else
%p A291022          fi:
%p A291022        od:
%p A291022       od:
%p A291022      od:
%p A291022      if it>0 and it = k1-1
%p A291022       then
%p A291022       printf(`%d, `,n):
%p A291022       else
%p A291022      fi:
%p A291022   od:
%Y A291022 Cf. A019434, A088723.
%K A291022 nonn
%O A291022 1,1
%A A291022 _Michel Lagneau_, Aug 31 2017