A355028 a(n) is the maximum number of distinct prime signatures of numbers with n prime divisors (counted with multiplicity) that have the same number of divisors.

1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 4, 4, 5, 5, 5, 6, 6, 7, 9, 9, 11, 12, 13, 14, 16, 17, 19, 23, 26, 30, 32, 35, 38, 40, 43, 51, 56, 62, 68, 74, 80, 86, 94, 106, 118, 128, 140, 152, 167, 179, 197, 221, 247, 272, 298, 325, 353, 384, 425, 473, 522, 567, 631

Offset: 0

Author

Amiram Eldar, Jun 16 2022

Keywords

• nonn

Examples

			a(8) = 2 since there are 2 prime signatures of numbers k with Omega(k) = 8, p1^5 * p2 * p3 * p4 and p1^3 * p2^3 * p3^2, that correspond to the same number of divisors, 48.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..90

Crossrefs

Cf. A000005, A001222, A101296, A118914, A355026, A355027.

Programs

Mathematica

a[n_] := Max[Tally[Times @@ (# + 1) & /@ IntegerPartitions[n]][[;; , 2]]]; Array[a, 50, 0]