A368825 a(1) = 1; for n > 1, a(n) = A055231(a(n-1) + n), where A055231(k) is the powerfree part of k.

1, 3, 6, 10, 15, 21, 7, 15, 3, 13, 3, 15, 7, 21, 1, 17, 34, 13, 1, 21, 42, 1, 3, 1, 26, 13, 5, 33, 62, 23, 2, 34, 67, 101, 17, 53, 10, 3, 42, 82, 123, 165, 13, 57, 102, 37, 21, 69, 118, 21, 1, 53, 106, 5, 15, 71, 1, 59, 118, 178, 239, 301, 91, 155, 55, 1, 17, 85, 154, 7, 78, 6, 79, 17, 23, 11

Offset

1,2

Comments

The sequence is conjectured to contain all the squarefree numbers; see A005117.

The fixed points begin 1, 7, 5759, 35435, 58403, 62051, 182363, 261763, ... , although it is likely there are infinitely more.

See A368827 for the indices where a(n) = 1.

Links

Scott R. Shannon, Table of n, a(n) for n = 1..10000

Scott R. Shannon, Image of the first 1000000 terms. The green line is a(n) = n.

Example

a(9) = 3 as a(8)+9 = 15+9 = 24 = 2*2*2*3, and the powerfree part of 24 is 3.

Crossrefs

Cf. A368827, A368823 (multiplication), A055231, A005117, A124010.

Sequence in context: A096895 A034175 A361670 * A306698 A139131 A130485

Adjacent sequences: A368822 A368823 A368824 * A368826 A368827 A368828

Keyword

nonn

Author

Scott R. Shannon, Jan 07 2024

Status

approved