A358209 a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier that shares a factor with A024916(n-1) = Sum_{k=1..n-1} sigma(k).

1, 2, 4, 6, 3, 7, 9, 41, 8, 12, 15, 11, 127, 18, 5, 14, 10, 16, 277, 21, 24, 28, 22, 431, 491, 20, 26, 30, 25, 23, 27, 32, 857, 35, 42, 19, 33, 34, 13, 36, 38, 40, 37, 39, 44, 45, 46, 43, 48, 1987, 50, 52, 51, 54, 56, 57, 58, 60, 49, 62, 55, 64, 61, 63, 82, 66, 3631, 69, 17, 72, 65, 70, 68, 74

Offset: 1

Author

Scott R. Shannon, Nov 04 2022

Keywords

• nonn

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.

Examples

			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.
		

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.

Crossrefs

Cf. A358208, A024916, A000203, A356851, A064413.