A243984 Sum of non-twin divisors of n.

1, 3, 0, 1, 6, 8, 8, 9, 9, 18, 12, 12, 14, 24, 15, 25, 18, 35, 20, 36, 28, 36, 24, 36, 31, 42, 36, 50, 30, 63, 32, 57, 44, 54, 36, 75, 38, 60, 52, 66, 42, 92, 44, 78, 69, 72, 48, 100, 57, 93, 68, 92, 54, 116, 72, 114, 76, 90, 60, 125, 62, 96, 84, 121, 84, 140, 68, 120

Offset: 1

Author

Juri-Stepan Gerasimov, Jun 16 2014

Keywords

• nonn
• easy

Comments

See A243917 for definition of non-twin divisor.

Examples

			The divisors of 40 are 1, 2, 4, 5, 8, 10, 20, 40. Of these, 1, 5, 20, 40 are non-twin divisors. So a(40) = the sum of these divisors, which is 66.
		

Links

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

Crossrefs

Cf. A000203, A132882, A243917, A243983.

Programs

Maple

f:= proc(n) local d; d:= numtheory[divisors](n); convert(d minus map(`+`,d,2) minus map(`+`,d,-2),`+`) end proc:
map(f, [$1..100]); # Robert Israel, Aug 17 2014

Mathematica

a243984[n_Integer] := Total[Select[Divisors[n], If[And[# <= 2 || Divisible[n, # - 2] == False, Divisible[n, # + 2] == False], True, False] &]]; a243984 /@ Range[68] (* Michael De Vlieger, Aug 17 2014 *)

PARI

a(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, print1(a(n), ", ")) \\ Colin Barker, Jun 29 2014

Formula

a(n) = A000203(n) - A243983(n).