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 proper divisors of all previous terms is a prime number. In the first 10000 terms there are twenty-eight fixed points: 4, 5, 6, ..., 2486, 3280, 3292.

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

LINKS

Scott R. Shannon, Image of the first 10000 terms where a(n) is less than 110% of n. The green line is a(n) = n.

EXAMPLE

a(7) = 8 as Sum_{k=1..6} A001065(k) = 0 + 1 + 1 + 3 + 1 + 6 = 12, and 8 is the smallest unused number that shares a factor with 12.

CROSSREFS

KEYWORD

nonn

AUTHOR

Scott R. Shannon, Nov 04 2022

STATUS

approved