Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #18 Aug 21 2014 20:42:44
%S 1,3,4,8,9,16,20,22,24,27,35,48,64,90,94,115,119,143,170,171,192,200,
%T 214,216,217,265,310,322,323,343,382,497,517,527,656,679,710,729,742,
%U 745,782,862,889,899,935,970,1066,1174,1177,1207,1219,1270,1393,1426
%N Numbers n such that A243984(n), the sum of non-twin divisors of n, is a square.
%C See A243917 for definition of non-twin divisor.
%C Squares included in the sequence are : 1, 4, 9, 16, 64, 729, ...
%H Michael De Vlieger, <a href="/A243985/b243985.txt">Table of n, a(n) for n = 1..8692</a> (a(n) < 5,000,000)
%e The positive divisors of 8 are 1, 2, 4, 8. Of these, 1 and 8 are non-twin divisors. So 8 is in this sequence, which is 1 + 8 = 3^2.
%t a243984[n_Integer] := Total[Select[Divisors[n], If[And[# <= 2 || Divisible[n, # - 2] == False, Divisible[n, # + 2] == False], True, False] &]]; a243985[n_Integer] := Flatten@Select[Position[Sqrt[a243984 /@ Range[n]], _?IntegerQ], If[Length[#] == 1, True, False] &]; a243985[1500] (* _Michael De Vlieger_, Aug 17 2014 *)
%o (PARI)
%o A243984(n) = s=0; fordiv(n, d, if(!((d>2 && n%(d-2)==0) || (d<=n-2 && n%(d+2)==0)), s+=d)); s
%o for(n=1, 200, if(issquare(A243984(n)), print1(n, ", "))) \\ _Colin Barker_, Jun 29 2014
%Y Cf. A006532, A243917 , A243984.
%K nonn
%O 1,2
%A _Juri-Stepan Gerasimov_, Jun 16 2014
%E Several terms corrected by _Colin Barker_, Jun 29 2014