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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.
2
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
1,1
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.
LINKS
EXAMPLE
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.
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 *)
CROSSREFS
Sequence in context: A315755 A315756 A315757 * A315758 A315759 A315760
KEYWORD
nonn
AUTHOR
Chuck Seggelin (seqfan(AT)plastereddragon.com), Jan 15 2005
STATUS
approved