STATUS
proposed
approved
The OEIS is supported by the many generous donors to the OEIS Foundation.
proposed
approved
editing
proposed
More generally: let tau[k](n) denote the number of ordered factorizations of n as a product of k terms, also named the k-th Piltz function (see A007425), then we have for n>1:
a(n) = Sum_{j=1..bigomega(n)} Sum_{k=1..j} (-1)^(j-k)*binomial(j,k)*tau[k](n), for n>1;or
a(n) = Sum_{j=1..bigomega(n)} Sum_{k=0..j-1} (-1)^k*binomial(j,k)*tau[j-k](n), for n>1. (End)
proposed
editing
editing
proposed
If p,q are distinct primes, and n,m>0 then we have :
a(p^n*q^m) = Sum_{k=0..min(n,m)} 2^(n+m-k-1)*binomial(n,k)*binomial(m,k) ;
More generally : let tau[k](n) denote the number of ordered factorizations of n as a product of k terms, also named the k-th Piltz function (see A007425), then we have :
proposed
editing
editing
proposed
(SageSageMath)
proposed
editing
editing
proposed
Kristin DeVleming and Nikita Singh, <a href="https://arxiv.org/abs/2311.15922">Rational unicuspidal plane curves of low degree</a>, arXiv:2311.15922 [math.AG], 2023. See p. 14.
proposed
editing
editing
proposed