A358175 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(a(k)), where A001065(m) is the sum of the proper divisors of m.

1, 2, 3, 4, 5, 6, 8, 19, 10, 7, 29, 9, 12, 14, 15, 18, 16, 20, 127, 22, 24, 26, 28, 21, 233, 13, 25, 241, 11, 27, 30, 32, 35, 33, 17, 34, 36, 433, 31, 39, 38, 40, 42, 44, 45, 48, 727, 46, 50, 797, 49, 52, 51, 54, 57, 37, 60, 56, 55, 58, 62, 63, 1259, 64, 66, 69, 68, 70, 65, 1579, 72, 78, 77, 74

Offset

1,2

Comments

The sequence is conjectured to be a permutation of the positive integers. In the first 10000 terms, other than the first three terms, there are thirty-five fixed points, the last being 2051. It is plausible no more exist although this is unknown.

Links

Table of n, a(n) for n=1..74.

Example

a(9) = 10 as Sum_{k=1..8} A001065(a(k)) = 0 + 1 + 1 + 3 + 1 + 6 + 7 + 1 = 20, and 10 is the smallest unused number that shares a factor with 20.

Crossrefs

Cf. A001065, A027751, A358082, A064413, A356851, A356430, A354960.

Sequence in context: A133706 A081710 A364455 * A241947 A128421 A115885

Adjacent sequences: A358172 A358173 A358174 * A358176 A358177 A358178

Keyword

nonn

Author

Scott R. Shannon, Nov 02 2022

Status

approved