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

1,1

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.

Links

Table of n, a(n) for n=1..50.

Formula

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

Example

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).

Mathematica

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

Crossrefs

Intersection of A001105 and (A238443 = A174973).

Subsequence of A071562 and of A319796.

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

Sequence in context: A051787 A050804 A081324 * A190787 A018229 A365265

Adjacent sequences: A361900 A361901 A361902 * A361904 A361905 A361906

Keyword

nonn

Author

Hartmut F. W. Hoft, Mar 28 2023

Status

approved