A243985 Numbers n such that A243984(n), the sum of non-twin divisors of n, is a square.

1, 3, 4, 8, 9, 16, 20, 22, 24, 27, 35, 48, 64, 90, 94, 115, 119, 143, 170, 171, 192, 200, 214, 216, 217, 265, 310, 322, 323, 343, 382, 497, 517, 527, 656, 679, 710, 729, 742, 745, 782, 862, 889, 899, 935, 970, 1066, 1174, 1177, 1207, 1219, 1270, 1393, 1426

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 16 2014

Keywords

• nonn

Comments

See A243917 for definition of non-twin divisor.

Squares included in the sequence are : 1, 4, 9, 16, 64, 729, ...

Examples

			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.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..8692 (a(n) < 5,000,000)

Crossrefs

Cf. A006532, A243917 , A243984.

Programs

Mathematica

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 *)

PARI

A243984(n) = s=0; fordiv(n, d, if(!((d>2 && n%(d-2)==0) || (d<=n-2 && n%(d+2)==0)), s+=d)); s
for(n=1, 200, if(issquare(A243984(n)), print1(n, ", "))) \\ Colin Barker, Jun 29 2014

Extensions

Several terms corrected by Colin Barker, Jun 29 2014