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A361903
Numbers k for which sqrt(k/2) divides k and the symmetric representation of sigma(k) has a single part.
2
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.
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.
Sequence in context: A051787 A050804 A081324 * A190787 A018229 A365265
KEYWORD
nonn
AUTHOR
Hartmut F. W. Hoft, Mar 28 2023
STATUS
approved