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A243865
Number of twin divisors of n.
5
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, 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, 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
OFFSET
1,3
COMMENTS
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.
LINKS
FORMULA
a(n) = A000005(n) - A243917(n).
a(3n) > 1 for all n >= 1.
a(A099477(n)) = 0, a(A059267(n)) > 0.
A099475(n) <= a(n) <= A000005(n).
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
EXAMPLE
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.
PROG
(PARI) a(n) = sumdiv(n, d, ((d>2) && !(n % (d-2))) || !(n % (d+2))); \\ Michel Marcus, Jun 25 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved