A336760 a(0) = 0; for n > 0, a(n) = a(n-1) - tau(n) if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + tau(n), where tau(n) is the number of divisors of n.

0, 1, 3, 5, 2, 4, 8, 6, 10, 7, 11, 9, 15, 13, 17, 21, 16, 14, 20, 18, 12, 16, 20, 22, 30, 27, 23, 19, 25, 27, 35, 33, 39, 43, 47, 51, 42, 40, 36, 32, 24, 26, 34, 36, 42, 48, 44, 46, 56, 53, 59, 55, 49, 51, 59, 63, 71, 67, 71, 69, 57, 59, 63, 69, 62, 58, 50, 52, 58, 54, 62, 60, 72, 70, 66, 72

Offset

0,3

Comments

This sequences uses the same rules as Recamán's sequence A005132 except that, instead of adding or subtracting n each term, the number of divisors of n is used. See A000005.

For the first 10 million terms the smallest value not appearing is 28. The data indicate that a(n)/n approaches 1 as n goes to infinity. As tau(n) <= 2*sqrt(n) (see A046522), it implies that 28 and other small unvisited values will never be visited.

In the same range the maximum value is a(9998226) = 10987569, and 2202001 terms repeat a previously visited value, the first time this occurs is a(21) = a(16) = 16. The longest run of consecutive increasing terms is 30, starting at a(1115610) = 1217112, while the longest run of consecutive decreasing terms is 534, starting at a(9960335) = 10946233.

Links

Table of n, a(n) for n=0..75.

Index entries for sequences related to Recamán's sequence.

Example

a(2) = 3. As 2 has two divisors, a(2) = a(1) + 2 = 1 + 2 = 3.
a(4) = 2. As 4 has three divisors, and as 2 has not been previously visited and is nonnegative, a(4) = a(3) - 3 = 5 - 3 = 2.

Crossrefs

Cf. A005132, A000005, A046522, A336761.

Sequence in context: A082817 A084753 A163364 * A082822 A109313 A331526

Adjacent sequences: A336757 A336758 A336759 * A336761 A336762 A336763

Keyword

nonn

Author

Scott R. Shannon, Aug 03 2020

Status

approved