OFFSET

1,2

COMMENTS

The majority of terms lie just above the line a(n) = n, although a small number of terms are significantly larger due to having to share a factor with numerous previous terms, some of which are prime, e.g., a(6254) = 4501732178.

In the first 10000 terms the fixed points are 1, 2, 10, 65, 1261, 6527, although more likely exist. The sequences is conjectured to be a permutation of the positive integers. Unlike A064413 the primes do not occur in their natural order.

LINKS

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

EXAMPLE

a(4) = 6 as 6 shares a factor with a(3) = 4 and also shares a factor with a(2) = 2 which is required as a(2+a(2)) = a(4) = 6.

a(8) = 15 as 15 shares a factor with a(7) = 12 and also shares a factor with a(5) = 3 which is required as a(5+a(5)) = a(8) = 15. Note that 8 shares a factor with 12 but it does not share a factor with 3, so a(8) cannot be 8. This is the first term to differ from A064413.

CROSSREFS

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Sep 03 2023

STATUS

approved