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%I #60 Jan 08 2021 10:53:34
%S 1,2,3,4,5,7,8,11,13,16,17,19,23,29,31,32,37,41,43,47,53,59,61,64,67,
%T 71,73,79,83,89,97,101,103,107,109,113,127,128,131,137,139,149,151,
%U 157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,256
%N Powers of 2 and odd primes; alternatively, numbers that cannot be written as a sum of at least three consecutive positive integers.
%C From _Omar E. Pol_, Feb 24 2014: (Start)
%C Also the odd noncomposite numbers (A006005) and the powers of 2 with positive exponent, in increasing order.
%C If a(n) is composite and a(n) - a(n-1) = 1 then a(n-1) is a Mersenne prime (A000668), hence a(n-1)*a(n)/2 is a perfect number (A000396) and a(n-1)*a(n) equals the sum of divisors of a(n-1)*a(n)/2.
%C If a(n) is even and a(n+1) - a(n) = 1 then a(n+1) is a Fermat prime (A019434). (End)
%H Robert Israel, <a href="/A174090/b174090.txt">Table of n, a(n) for n = 1..10000</a>
%H Jaap Spies, <a href="http://www.jaapspies.nl/bookb5.pdf">A Bit of Math, The Art of Problem Solving</a>, Jaap Spies Publishers (2019).
%H Nieuw Archief voor Wiskunde, <a href="http://www.jaapspies.nl/mathfiles/problem2005-2C.pdf">Problems/UWC, Problem C</a>, Vol. 5/6, No. 2.
%p N:= 300: # to get all terms <= N
%p S:= {seq(2^i,i=0..ilog2(N))} union select(isprime,{ 2*i+1 $ i=1..floor((N-1)/2) }):
%p sort(convert(S,list)); # _Robert Israel_, Jun 18 2015
%t a[n_] := Product[GCD[2 i - 1, n], {i, 1, (n - 1)/2}] - 1;
%t Select[Range[242], a[#] == 0 &] (* _Gerry Martens_, Jun 15 2015 *)
%Y Numbers not in A111774.
%Y Equals A000079 UNION A065091.
%Y Equals A067133 \ {6}.
%Y Cf. A000040, A000203, A000396, A000668, A006005, A019434, A092506.
%Y Cf. also A138591, A174069, A174070, A174071.
%K nonn
%O 1,2
%A _Vladimir Joseph Stephan Orlovsky_, Mar 07 2010, and _Omar E. Pol_, Feb 24 2014
%E This entry is the result of merging an old incorrect entry and a more recent correct version. _N. J. A. Sloane_, Dec 07 2015
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