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

0,9

Links

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

Example

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.

Mathematica

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

Crossrefs

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

Sequence in context: A057366 A189663 A341440 * A061375 A029920 A100719

Adjacent sequences: A355025 A355026 A355027 * A355029 A355030 A355031

Keyword

nonn

Author

Amiram Eldar, Jun 16 2022

Status

approved