A368823 -id:A368823 - cp's OEIS frontend

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

Scott R. Shannon, Jan 07 2024

nonn

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.

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

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.

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

A368827 Indices k where A368825(k) = 1.

Original entry on oeis.org

1, 15, 19, 22, 24, 51, 57, 66, 86, 89, 122, 127, 134, 179, 183, 224, 265, 287, 288, 326, 368, 402, 425, 455, 458, 461, 530, 535, 650, 668, 674, 675, 687, 803, 825, 854, 890, 897, 953, 997, 1147, 1261, 1341, 1371, 1381, 1442, 1443, 1466, 1475, 1587, 1650, 1662, 1691, 1734, 1743, 1755, 1965

Offset: 1

Scott R. Shannon, Jan 07 2024

nonn

There are 2095 indices less than 2 million. In this range on fifteen occasions the indices are consecutive - these indices begin 287, 288, 674, 675, 1442, 1443, 3362, 3363, ... .

Scott R. Shannon, Table of n, a(n) for n = 1..2095

Cf. A368825, A368823, A055231, A005117, A124010.

cp's OEIS Frontend

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

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