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A103291 Numbers k such that sigma(2^k-1) >= 2*(2^k-1)-1, i.e., the number 2^k-1 is perfect, abundant, or least deficient.

%I A103291 #20 Jul 26 2025 03:32:31
%S A103291 1,12,24,36,40,48,60,72,80,84,90,96,108,120,132,140,144,156,160,168,
%T A103291 180,192,200,204,210,216,220,228,240,252,264,270,276,280,288,300,312,
%U A103291 320,324,330,336,348,360,372,384,396,400,408,420,432,440,444,450,456,468
%N A103291 Numbers k such that sigma(2^k-1) >= 2*(2^k-1)-1, i.e., the number 2^k-1 is perfect, abundant, or least deficient.
%C A103291 Is there an odd term besides 1? Numbers 2^a(i)-1 form set difference of sequences A103289 and A096399.
%C A103291 Odd terms > 1 exist, but there are none < 10^7. If k > 1 is an odd term, then 2^k-1 must have more than 900000 distinct prime factors and all of them must be members of A014663. - _David Wasserman_, Apr 15 2008
%H A103291 Amiram Eldar, <a href="/A103291/b103291.txt">Table of n, a(n) for n = 1..136</a>
%F A103291 Numbers k such that 2^k-1 is in A103288.
%o A103291 (PARI) for(i=1,1000,n=2^i-1;if(sigma(n)>=2*n-1,print1(i, ", ")));
%Y A103291 Cf. A000203, A075708, A103288, A103289, A103292, A023196.
%K A103291 hard,nonn
%O A103291 1,2
%A A103291 _Max Alekseyev_, Jan 28 2005
%E A103291 More terms from _David Wasserman_, Apr 15 2008