A102883 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.

6, 12, 18, 24, 28, 36, 40, 42, 45, 48, 50, 54, 56, 60, 66, 70, 72, 75, 78, 80, 90, 96, 98, 100, 102, 110, 112, 114, 117, 120, 126, 130, 132, 135, 138, 144, 150, 154, 156, 160, 162, 165, 170, 174, 176, 180, 186, 190, 192, 196, 198, 200, 204, 208, 210, 216, 220

Offset: 1

Author

Chuck Seggelin (seqfan(AT)plastereddragon.com), Jan 15 2005

Keywords

• nonn

Comments

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.

Examples

			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.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A070039, A102884.

Programs

Maple

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;

Mathematica

aQ[n_] := GCD[n, DivisorSum[n, # &, # < Sqrt[n] &]] > 1; Select[Range[220], aQ] (* Amiram Eldar, Aug 28 2019 *)