A358209 -id:A358209 - cp's OEIS frontend

A358208 a(1) = 1; a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} A001065(k), where A001065(k) is the sum of the proper divisors of k.

1, 2, 3, 4, 5, 6, 8, 13, 10, 9, 12, 11, 7, 14, 15, 18, 16, 17, 20, 107, 21, 22, 24, 25, 191, 197, 27, 26, 28, 30, 33, 32, 35, 34, 36, 29, 38, 433, 39, 40, 42, 523, 577, 44, 45, 31, 677, 46, 48, 50, 23, 49, 52, 51, 54, 56, 55, 63, 43, 58, 37, 57, 53, 60, 66, 61, 62, 70, 68, 64, 65, 69, 71, 75, 80

Offset: 1

Scott R. Shannon, Nov 04 2022

nonn

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.

			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.

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.

Cf. A358209, A001065, A024916, A000203, A356851, A064413.

cp's OEIS Frontend

A358208 a(1) = 1; a(2) = 2; a(3) = 3; for n > 3, a(n) is the smallest positive number not occurring earlier that shares a factor with Sum_{k=1..n-1} A001065(k), where A001065(k) is the sum of the proper divisors of k.

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