A243865 Number of twin divisors of n.

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

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

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

Cf. A000005, A002162, A099475, A132747, A243917.

Sequence in context: A316344 A122157 A080378 * A120439 A248512 A352564

Adjacent sequences: A243862 A243863 A243864 * A243866 A243867 A243868

Keyword

nonn

Author

Juri-Stepan Gerasimov, Jun 13 2014

Status

approved