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%I #17 May 05 2023 21:52:25
%S 2,8,18,32,72,128,162,200,288,392,450,512,648,800,882,968,1152,1352,
%T 1458,1568,1800,2048,2178,2592,3042,3200,3528,3872,4050,4608,5000,
%U 5202,5408,5832,6272,6498,7200,7938,8192,8712,9248,9522,9800,10368,11250,11552,12168,12800,13122,14112
%N Numbers k for which sqrt(k/2) divides k and the symmetric representation of sigma(k) has a single part.
%C Every number in this sequence has the form 2^(2*i + 1) * k^(2*j), i,j>=0, k>=1.
%C The number of 1's in row a(n) of the triangle in A237048 as well as the length of that row are odd.
%F a(n) = k when A001105(n) = k and A237271(k) = 1.
%e a(4) = 32 has 4 as its single middle divisor, and its symmetric representation of sigma consists of one part of width 1.
%e a(9) = 288 = 2^5 * 3^2 has 3 middle divisors - 12 = 2^2 * 3 , 16 = 2^4, 18 = 2 * 3^2 - and its symmetric representation of sigma consists of one part, the section of maximum width 3 of the single part includes the diagonal (see also A250068).
%t (* Function a237271[ ] is defined in A237271 *)
%t a361903[n_] := Select[Range[n], IntegerQ[#/Sqrt[#/2]]&&a237271[#]==1&]
%t a361903[15000]
%Y Intersection of A001105 and (A238443 = A174973).
%Y Subsequence of A071562 and of A319796.
%Y Cf. A235791, A237048, A237270, A237271, A237593, A250068.
%K nonn
%O 1,1
%A _Hartmut F. W. Hoft_, Mar 28 2023
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