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%I #20 Aug 19 2014 01:01:12
%S 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,
%T 36,50,30,63,32,57,44,54,36,75,38,60,52,66,42,92,44,78,69,72,48,100,
%U 57,93,68,92,54,116,72,114,76,90,60,125,62,96,84,121,84,140,68,120
%N Sum of non-twin divisors of n.
%C See A243917 for definition of non-twin divisor.
%H Jens Kruse Andersen, <a href="/A243984/b243984.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000203(n) - A243983(n).
%e 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.
%p f:= proc(n) local d; d:= numtheory[divisors](n); convert(d minus map(`+`,d,2) minus map(`+`,d,-2),`+`) end proc:
%p map(f, [$1..100]); # _Robert Israel_, Aug 17 2014
%t 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 *)
%o (PARI)
%o a(n) = s=0; fordiv(n, d, if(!((d>2 && n%(d-2)==0) || (d<=n-2 && n%(d+2)==0)), s+=d)); s
%o for(n=1, 200, print1(a(n), ", ")) \\ _Colin Barker_, Jun 29 2014
%Y Cf. A000203, A132882, A243917, A243983.
%K nonn,easy
%O 1,2
%A _Juri-Stepan Gerasimov_, Jun 16 2014
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