A243984 -id:A243984 - cp's OEIS frontend

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

Juri-Stepan Gerasimov, Jun 16 2014

nonn

See A243917 for definition of non-twin divisor.

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

			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.

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

Cf. A006532, A243917 , A243984.

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 *)

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

Several terms corrected by Colin Barker, Jun 29 2014

A243983 Sum of twin divisors of n.

Original entry on oeis.org

0, 0, 4, 6, 0, 4, 0, 6, 4, 0, 0, 16, 0, 0, 9, 6, 0, 4, 0, 6, 4, 0, 0, 24, 0, 0, 4, 6, 0, 9, 0, 6, 4, 0, 12, 16, 0, 0, 4, 24, 0, 4, 0, 6, 9, 0, 0, 24, 0, 0, 4, 6, 0, 4, 0, 6, 4, 0, 0, 43, 0, 0, 20, 6, 0, 4, 0, 6, 4, 12, 0, 24, 0, 0, 9, 6, 0, 4, 0, 24, 4, 0, 0, 42, 0, 0, 4, 6, 0, 9

Offset: 1

Juri-Stepan Gerasimov, Jun 16 2014

nonn

See A243865 for definition of twin divisor.

			The positive divisors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Of these, 2, 4, 8, 10, are twin divisors. So a(40) = the sum of these divisors, which is 24.

Jens Kruse Andersen, Table of n, a(n) for n = 1..10000

Cf, A000203, A132748, A243865.

a(n) = A000203(n) - A243984(n).

cp's OEIS Frontend

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

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