A389610 Same as A389609, except only consider prime divisors, instead of all divisors.

2, 4, 6, 9, 12, 14, 17, 19, 26, 43, 62, 64, 77, 120, 122, 153, 155, 162, 173, 175, 178, 183, 185, 246, 249, 266, 271, 302, 304, 307, 480, 485, 492, 494, 583, 586, 647, 652, 689, 691, 694, 735, 738, 821, 823, 830, 849, 1120, 1122, 1273, 1275, 1294, 1601, 1603, 1606, 1611, 1616, 1713, 1715, 1718, 1759, 1761, 1774, 1793, 1804

Offset

1,1

Comments

Let D(k) = list of the distinct prime 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 integers > 1 which is equal to the partial sums of C.

We start with 2, since 1 has no prime divisors. If a(1)=2, a(2)=3 does not work. If a(1)=2 and a(2)=4, a(3)=5 does not work, but a(1)=2, a(2)=4, a(3)=6 gives C = [2, 2, 2, 3,...] with partial sums [2, 4, 6, 9, ...], and we can take a(4) = 9, and from this point on the sequence is uniquely determined by its existing terms.

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..10000

Crossrefs

Cf. A389395, A389609.

Sequence in context: A183422 A025057 A189753 * A278450 A030763 A387073

Adjacent sequences: A389607 A389608 A389609 * A389611 A389612 A389613

Keyword

nonn

Author

N. J. A. Sloane, Oct 12 2025.

Status

approved