A389482 Prime powers q such that LCM(1,2,...,q) = A003418(q) is highly abundant (A002093).

1, 2, 3, 4, 5, 7, 8, 9, 11, 13, 16, 17, 19, 23, 25, 27, 29, 31, 32, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 81, 83, 89, 125, 127, 128, 131, 137, 139, 169

Offset

1,2

Comments

Sequence resulted from a collaborative project at MathOverflow, see Tao et al. (2025) link.

Since values of A003418(m) change at prime powers, A003418(m) is highly abundant (A002093) if the largest prime power q <= m belongs to this sequence. Such m are listed in A389483.

Links

Table of n, a(n) for n=1..39.

L. Alaoglu and P. Erdős, On Highly Composite and Similar Numbers, Transactions of the American Mathematical Society 56:3 (1944), 448-469.

Terry Tao et al., Is the least common multiple sequence lcm(1, 2, ..., n) a subset of the highly abundant numbers?, MathOverflow, 2025.

Crossrefs

Subsequence of A000961.

Cf. A003418, A002093, A389483.

Sequence in context: A000961 A128603 A195943 * A096165 A164336 A348263

Adjacent sequences: A389479 A389480 A389481 * A389483 A389484 A389485

Keyword

nonn,nice,fini,full

Author

Max Alekseyev, Oct 05 2025

Status

approved