%I #5 Aug 28 2019 17:00:15
%S 5,14,18,28,44,48,52,54,55,56,68,72,76,77,85,88,91,92,95,96,104,119,
%T 125,133,145,153,154,168,171,175,182,187,190,200,203,207,209,217,222,
%U 225,230,234,238,240,245,246,248,250,253,258,261,264,266,275,279,282,287
%N a(n) * 6 does not appear in A102883.
%C Many of these are excluded because the sum of a(n)*6 and its divisors less than or equal to its square root is prime, but not always. a(3) = 18. 18*6 = 108. Adding the divisors less than or equal to the square root of 108 yields 133. 133 is not prime, but shares no common divisor with 108 greater than 1.
%H Amiram Eldar, <a href="/A102884/b102884.txt">Table of n, a(n) for n = 1..10000</a>
%e a(2) = 14 because 14*6 is 84. The divisors of 84 which are less than or equal to its square root are 1, 2, 3, 4, 6 and 7. 84+1+2+3+4+6+7 = 107. GCD(84,107)=1, so 84 is excluded from A102883. Most multiples of 6 are included in A102883, 14*6 is the second multiple to be excluded.
%t aQ[n_] := GCD[6n, DivisorSum[6n, # &, # < Sqrt[6n] &]] == 1; Select[Range[287], aQ] (* _Amiram Eldar_, Aug 28 2019 *)
%Y Cf. A102883.
%K nonn
%O 1,1
%A Chuck Seggelin (seqfan(AT)plastereddragon.com), Jan 15 2005