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

Author

Neal Gersh Tolunsky, Feb 02 2025

Keywords

• nonn

Comments

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

Examples

			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.
		

Links

• Dominic McCarty, Table of n, a(n) for n = 1..10000
• Dominic McCarty, Java program for A380783

Crossrefs

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