OFFSET
0,2
COMMENTS
If D_n = {p^0, ..., p^n} is the set of all positive divisors of p^n (p is a prime), then a(n) gives the number of all subsets of D_n for which the product of all their elements is a divisor of p^n. Furthermore, a(n) gives the number of all strict partitions of n including the integer 0.
LINKS
Hiroaki Yamanouchi, Table of n, a(n) for n = 0..1000
FORMULA
a(n) = -1 + 2*Sum_{k=0..n} a*(k) where a*(n) = A000009(n).
a(n) = A248955(p^n), where p is any prime. - Michel Marcus, Nov 07 2014
a(n) = 2*A036469(n) - 1. - Hiroaki Yamanouchi, Nov 21 2014
EXAMPLE
a(1) = 3: -p*x+p; -x+p; x^2 - (p+1)*x + p.
CROSSREFS
KEYWORD
nonn
AUTHOR
Reiner Moewald, Oct 17 2014
EXTENSIONS
a(20)-a(22) from Michel Marcus, Nov 07 2014
a(23)-a(47) from Hiroaki Yamanouchi, Nov 21 2014
STATUS
approved