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

1,2

Comments

See A243917 for definition of non-twin divisor.

Links

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

Formula

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A000203, A132882, A243917, A243983.

Sequence in context: A111924 A212880 A211510 * A100485 A143397 A341856

Adjacent sequences: A243981 A243982 A243983 * A243985 A243986 A243987

Keyword

nonn,easy

Author

Juri-Stepan Gerasimov, Jun 16 2014

Status

approved