A389609 Lexicographically earliest infinite sequence of distinct positive integers with the property that the partial sums of the concatenation of the divisors of the terms is the sequence itself.

1, 2, 4, 5, 7, 11, 12, 17, 18, 25, 26, 37, 38, 40, 43, 47, 53, 65, 66, 83, 84, 86, 89, 95, 104, 122, 123, 128, 153, 154, 156, 169, 195, 196, 233, 234, 236, 255, 293, 294, 296, 300, 305, 313, 323, 343, 383, 384, 427, 428, 475, 476, 529, 530, 535, 548, 613, 614, 616, 619, 625, 636, 658, 691, 757, 758, 841, 842, 844, 847, 851, 857, 864

Offset

1,2

Comments

Let D(k) = list of the divisors of k in increasing order, and let C = [D(a(1)), D(a(2)), D(a(3)), ...]. The sequence is the lexicographically earliest sequence of positive integers which is equal to the partial sums of C.

Inspired by A389395, which is a similar sequence based on proper divisors.

Links

N. J. A. Sloane, Table of n, a(n) for n = 1..11482

Example

After a(1)=1, a(2)=2, we have C = [1, 1, 2, ...] with partial sums [1, 2, 4, ...], which suggests taking a(3) = 4, which would give C = [1,1,2,1,2,4,...] with partial sums [1,2,4,5,7,11, ...], which would suggest taking a(4), a(5), a(6) = 5,7,11. From this point on the sequence extends itself uniquely. This is the earliest possible extension, and so IS the sequence.

Crossrefs

Cf. A389395.

Sequence in context: A082741 A288349 A099522 * A255850 A108464 A394407

Adjacent sequences: A389606 A389607 A389608 * A389610 A389611 A389612

Keyword

nonn

Author

N. J. A. Sloane, Oct 12 2025

Status

approved