A355032 a(n) is the maximum number of prime signatures of numbers with n divisors that have the same number of prime divisors (counted with multiplicity).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1

Offset

1,36

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(A355033(n)) = n.

Example

a(2) = 1 since the numbers with 2 divisors are all primes and thus have only 1 prime signature.
a(36) = 2 since numbers with 36 divisors have 2 prime signatures, p1^5 * p2^5 and p1 * p2 * p3^8, that correspond to numbers with 10 prime divisors (counted with multiplicity).
a(72) = 3 since numbers with 72 divisors have 3 prime signatures, p1 * p2^5 * p3^5, p1^2 * p2^2 * p3^7 and p1 * p2 * p3 * p4^8, that correspond to numbers with 11 prime divisors (counted with multiplicity).

Mathematica

Table[Max[Tally[Total[#-1]& /@ f[n]][[;; , 2]]], {n, 1, 100}] (* using the function f by T. D. Noe at A162247 *)

Crossrefs

Cf. A000005, A001222, A118914, A162247, A355028, A355030, A355031, A355033.

Sequence in context: A214710 A120888 A031230 * A244226 A344590 A111616

Adjacent sequences: A355029 A355030 A355031 * A355033 A355034 A355035

Keyword

nonn

Author

Amiram Eldar, Jun 16 2022

Status

approved