A335382 a(0) = 0, a(1) = 1; for n > 1, a(n) = a(n-1) - sigma(n) if nonnegative and not already in the sequence, otherwise a(n) = a(n-1) + sigma(n), where sigma(n) is the sum of the divisors of n.

0, 1, 4, 8, 15, 9, 21, 13, 28, 41, 23, 11, 39, 25, 49, 73, 42, 24, 63, 43, 85, 53, 17, 41, 101, 70, 112, 72, 16, 46, 118, 86, 149, 197, 143, 95, 186, 148, 88, 32, 122, 80, 176, 132, 48, 126, 54, 6, 130, 187, 94, 22, 120, 66, 186, 114, 234, 154, 64, 124, 292, 230, 134, 30, 157, 241, 97, 29, 155

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 sum of the divisors of n is used. See A000203.

For the first 10 million terms the smallest value not appearing is 76. It is likely that all values are eventually visited, although this is unknown.

In the same range the maximum value is a(9297600) = 93571073, and 402979 terms repeat a previously visited value, the first time this occurs is a(23) = a(9) = 41. The longest run of consecutive increasing terms is 5, starting at a(105187) = 25833, while the longest run of consecutive decreasing terms is 7, starting at a(6826248) = 83016261.

Links

Table of n, a(n) for n=0..68.

Example

a(2) = 4. As sigma(2) = 3, and a(1)<3, a(2) = a(1) + 3 = 4.
a(4) = 15. As sigma(4) = 7, and 1 has previously appeared, a(4) = a(3) + 7 = 15.
a(5) = 9. As sigma(5) = 6, and 9 has not previously appeared, a(5) = a(4) - 6 = 9.

Crossrefs

Cf. A005132, A000203, A335372, A336760, A336761, A000040.

Sequence in context: A272048 A112312 A076343 * A272346 A354846 A214440

Adjacent sequences: A335379 A335380 A335381 * A335383 A335384 A335385

Keyword

nonn

Author

Scott R. Shannon, Aug 16 2020

Status

approved