A361903 Numbers k for which sqrt(k/2) divides k and the symmetric representation of sigma(k) has a single part.

2, 8, 18, 32, 72, 128, 162, 200, 288, 392, 450, 512, 648, 800, 882, 968, 1152, 1352, 1458, 1568, 1800, 2048, 2178, 2592, 3042, 3200, 3528, 3872, 4050, 4608, 5000, 5202, 5408, 5832, 6272, 6498, 7200, 7938, 8192, 8712, 9248, 9522, 9800, 10368, 11250, 11552, 12168, 12800, 13122, 14112

Offset: 1

Author

Hartmut F. W. Hoft, Mar 28 2023

Keywords

• nonn

Comments

Every number in this sequence has the form 2^(2*i + 1) * k^(2*j), i,j>=0, k>=1.

The number of 1's in row a(n) of the triangle in A237048 as well as the length of that row are odd.

Examples

			a(4) = 32 has 4 as its single middle divisor, and its symmetric representation of sigma consists of one part of width 1.
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).
		

Crossrefs

Intersection of A001105 and A174973.

Subsequence of A071562 and of A319796.

Cf. A235791, A237048, A237270, A237271, A237593, A250068.

Programs

Mathematica

(* Function a237271[ ] is defined in A237271 *)
a361903[n_] := Select[Range[n], IntegerQ[#/Sqrt[#/2]]&&a237271[#]==1&]
a361903[15000]

Formula

a(n) = k when A001105(n) = k and A237271(k) = 1.