OFFSET

1,2

COMMENTS

The majority of terms are concentrated just below the line a(n) = n. However, some terms are much larger because the sum of the divisors of all previous terms is a prime number. In the first 5000 terms there are thirteen fixed points: 32, 52, 54, ..., 1331, 2082, 2097.

Conjecture: the sequence is a permutation of the positive integers.

LINKS

Scott R. Shannon, Image of the first 5000 terms where a(n) is less than 110% of n. The green line is a(n) = n.

EXAMPLE

a(5) = 3 as sigma(1) + sigma(2) + sigma(3) + sigma(4) = A024916(4) = 15, and 3 is the smallest unused number that shares a factor with 15.

CROSSREFS

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Nov 04 2022

STATUS

approved