A380783 Lexicographically earliest sequence of positive integers such that for any value k, no two sets of one or more indices at which k occurs have the same product.

1, 2, 2, 2, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 4, 2, 2, 3, 2, 4, 4, 3, 2, 4, 2, 3, 4, 5, 2, 4, 2, 5, 4, 3, 5, 5, 2, 3, 4, 6, 2, 5, 2, 5, 6, 3, 2, 6, 2, 3, 4, 5, 2, 3, 6, 4, 4, 3, 2, 5, 2, 3, 6, 3, 6, 7, 2, 5, 4, 6, 2, 6, 2, 3, 4, 5, 7, 7, 2, 7, 2, 3, 2, 5, 6, 3, 4

Offset

1,2

Comments

The Fermi-Dirac primes (A050376) are the indices of 2s in this sequence.

Links

Dominic McCarty, Table of n, a(n) for n = 1..10000

Dominic McCarty, Java program for A380783

Example

a(8) = 3: We cannot have 1 here because the set of indices i = 8 and i = 1,8 would have the same product. We cannot have a(8) = 2 because i = 8 would have the same product as i = 2,4. So a(8) = 3.

Crossrefs

Cf. A050376, A380751, A380921 (indices of records).

Sequence in context: A081309 A395633 A329377 * A010553 A262095 A163374

Adjacent sequences: A380780 A380781 A380782 * A380784 A380785 A380786

Keyword

nonn

Author

Neal Gersh Tolunsky, Feb 02 2025

Status

approved