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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.
2
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
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
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jun 16 2022
STATUS
approved