%I
%S 2,4,5,7,8,16,29,32,39,121,128,256,279,469,1299,3477,7299,7525,8192,
%T 13969,19262,19909,26739,31493,54722,65536,99381,131072,357699,524288,
%U 13204262,20742483,33550337,72873362
%N Numbers m such that there exist positive integers i <= m and j >= m such that m = Sum_{k=i..j} A001065(k), where A001065(k) = sum of the proper divisors of k, and i and j do not both equal m.
%C No perfect numbers are included as it is required i and j cannot both equal m. Any prime number that is one more than a perfect number will appear in the sequence.
%e 2 is a term as A001065(2) = 1, A001065(3) = 1, and 1 + 1 = 2.
%e 5 is a term as A001065(3) = 1, A001065(4) = 3, A001065(5) = 1, and 1 + 3 + 1 = 5.
%e 29 is a term as A001065(28) = 28, A001065(29) = 1, and 28 + 1 = 29. This is an example of a prime number one more than a perfect number, thus it will appear in the sequence.
%e 121 is a term as A001065(121) = 12, A001065(122) = 64, A001065(123) = 45, and 12 + 64 + 45 = 121.
%e 19262 is a term as A001065(19261) = 3203, A001065(19262) = 9634, A001065(19263) = 6425, and 3203 + 9634 + 6425 = 19262. This is the first term that requires i < m and j > m.
%Y Cf. A001065, A000396, A072188.
%K nonn,more
%O 1,1
%A _Scott R. Shannon_, Jul 05 2021
