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A243984 Sum of non-twin divisors of n. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)