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%I #30 Mar 22 2024 04:22:46
%S 0,0,2,2,0,2,0,2,2,0,0,5,0,0,3,2,0,2,0,2,2,0,0,6,0,0,2,2,0,3,0,2,2,0,
%T 2,5,0,0,2,4,0,2,0,2,3,0,0,6,0,0,2,2,0,2,0,2,2,0,0,8,0,0,4,2,0,2,0,2,
%U 2,2,0,6,0,0,3,2,0,2,0,4,2,0,0,7,0,0,2,2,0,3,0,2,2,0,0,6
%N Number of twin divisors of n.
%C A divisor m of n is a twin divisor if m-2 (for m >= 3) and m+2 (for m <= n-2) also divide n.
%H Jens Kruse Andersen, <a href="/A243865/b243865.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A000005(n) - A243917(n).
%F a(3n) > 1 for all n >= 1.
%F a(A099477(n)) = 0, a(A059267(n)) > 0.
%F A099475(n) <= a(n) <= A000005(n).
%F Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = log(2)/2 + 17/12 = 1.7632402569... . - _Amiram Eldar_, Mar 22 2024
%e The positive divisors of 20 are 1, 2, 4, 5, 10, 20. Of these, 2 and 4 are twin divisors: (2)+2 = 4, which divides n, and (4)-2 = 2 also divides n. So a(20) = the number of these divisors, which is 2.
%o (PARI) a(n) = sumdiv(n, d, ((d>2) && !(n % (d-2))) || !(n % (d+2))); \\ _Michel Marcus_, Jun 25 2014
%Y Cf. A000005, A002162, A099475, A132747, A243917.
%K nonn
%O 1,3
%A _Juri-Stepan Gerasimov_, Jun 13 2014
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