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%I #5 Aug 28 2019 16:35:24
%S 6,12,18,24,28,36,40,42,45,48,50,54,56,60,66,70,72,75,78,80,90,96,98,
%T 100,102,110,112,114,117,120,126,130,132,135,138,144,150,154,156,160,
%U 162,165,170,174,176,180,186,190,192,196,198,200,204,208,210,216,220
%N Terms which share a divisor greater than 1 with the value formed by adding them to the sum of their divisors less than or equal to their square roots.
%C At first glance it appears that all multiples of 6 are included in this sequence, but a number of them are excluded (such as 5*6 and 14*6.) See A102884 for a list of multiples of 6 not included in this sequence.
%H Amiram Eldar, <a href="/A102883/b102883.txt">Table of n, a(n) for n = 1..10000</a>
%e a(3) = 18 because the divisors of 18 less than or equal to its square root are 1, 2 and 3. 18+1+2+3 = 24 and GCD(18,24) = 6 which is greater than 1. 18 is the third term which satisfies this requirement.
%p compute := proc (n) local m, a; m := n; for a to n^.5 do if `mod`(n,a) = 0 then m := m+a end if end do; m end proc L:=[];for i from 1 to 2500 do; if i>0 then; x:=compute(i); if gcd(x,i) > 1 then L:=[op(L),i]; fi; fi; od;L;
%t aQ[n_] := GCD[n, DivisorSum[n, # &, # < Sqrt[n] &]] > 1; Select[Range[220], aQ] (* _Amiram Eldar_, Aug 28 2019 *)
%Y Cf. A070039, A102884.
%K nonn
%O 1,1
%A Chuck Seggelin (seqfan(AT)plastereddragon.com), Jan 15 2005
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