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
Keywords
Examples
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).
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
Formula
a(A355033(n)) = n.