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A319802 Even numbers without middle divisors.

%I A319802 #47 Oct 14 2021 03:54:10
%S A319802 10,14,22,26,34,38,44,46,52,58,62,68,74,76,78,82,86,92,94,102,106,114,
%T A319802 116,118,122,124,134,136,138,142,146,148,152,158,164,166,172,174,178,
%U A319802 184,186,188,194,202,206,212,214,218,222,226,230,232,236,244,246,248,250,254,258,262,268,274,278,282,284
%N A319802 Even numbers without middle divisors.
%C A319802 Even numbers k such that the symmetric representation of sigma(k) has an even number of parts.
%C A319802 For the definition of middle divisors, see A067742.
%C A319802 For more information about the symmetric representation of sigma(k) see A237593.
%C A319802 Let p be a prime > 5. Then a(n) is a number of the form m*p where m is an even number < sqrt(p). - _David A. Corneth_, Sep 28 2018
%C A319802 First differs from A244894 at a(51) = 230. - _R. J. Mathar_, Oct 04 2018
%C A319802 Is this twice A101550? - _Omar E. Pol_, Oct 04 2018
%C A319802 This sequence is not twice A101550: first differs at a(57) = 250 != 254 = 2*A101550(57). - _Michael S. Branicky_, Oct 14 2021
%H A319802 Michael S. Branicky, <a href="/A319802/b319802.txt">Table of n, a(n) for n = 1..10000</a>
%e A319802 10 is in the sequence because it's an even number and the symmetric representation of sigma(10) = 18 has an even number of parts as shown below:
%e A319802 .
%e A319802 .     _ _ _ _ _ _ 9
%e A319802 .    |_ _ _ _ _  |
%e A319802 .              | |_
%e A319802 .              |_ _|_
%e A319802 .                  | |_ _ 9
%e A319802 .                  |_ _  |
%e A319802 .                      | |
%e A319802 .                      | |
%e A319802 .                      | |
%e A319802 .                      | |
%e A319802 .                      |_|
%e A319802 .
%o A319802 (Python)
%o A319802 from sympy import divisors
%o A319802 def ok(n):
%o A319802     if n < 2 or n%2 == 1: return False
%o A319802     return not any(n//2 <= d*d < 2*n for d in divisors(n, generator=True))
%o A319802 print(list(filter(ok, range(285)))) # _Michael S. Branicky_, Oct 14 2021
%Y A319802 Intersection of A005843 and A071561.
%Y A319802 Cf. A244894 (a subsequence).
%Y A319802 Cf. A000203, A067742, A071090, A071562, A236104, A237270, A237271, A237593, A239932, A239934, A240542, A245092, A280919, A281007, A296508, A299761, A299777, A303297, A319529, A319796, A319801.
%K A319802 nonn
%O A319802 1,1
%A A319802 _Omar E. Pol_, Sep 28 2018