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A334740
Number of unordered factorizations of n with 3 different parts > 1.
2
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 1, 0, 1, 0, 0, 0, 4, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 5, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0, 4, 0, 0, 0, 1, 0, 4, 0, 0, 0, 0, 0, 8, 0, 0, 0, 1
OFFSET
1,48
COMMENTS
a(n) depends only on the prime signature of n. E.g. a(12)=a(75), since 12=2^2*3 and 75=5^2*3 share the same prime signature (2,1).
LINKS
EXAMPLE
a(48) = 3 = #{ (6,4,2), (8,3,2), (4,3,2,2) }.
PROG
(R)
maxe <- function(n, d) { i=0; while( n%%(d^(i+1))==0 ) { i=i+1 }; i }
uhRec <- function(n, l=1) {
uh = 0
if( n<=0 ) {
return(0)
} else if(n==1) {
return(ifelse(l==0, 1, 0))
} else if(l<=0) {
return(0)
} else if( (n>=2) && (l>=1) ) {
for(d in 2:n) {
m = maxe(n, d)
if(m>=1) for(i in 1:m) for(j in 1:min(i, l)) {
uhj = uhRec( n/d^i, l-j )
uh = uh + log(d)/log(n) * (-1)^(j+1) * choose(i, j) * uhj
}
}
return(round(uh, 3))
}
}
n=100; l=2; sapply(1:n, uhRec, l) # A334739
n=100; l=3; sapply(1:n, uhRec, l) # A334740
CROSSREFS
Cf. A334739 (2 different parts), A072670 (2 parts), A122179 (3 parts), A211159 (2 distinct parts), A122180 (3 distinct parts), A001055, A045778
Sequence in context: A335520 A326291 A269250 * A059484 A360016 A035678
KEYWORD
nonn
AUTHOR
Jacob Sprittulla, May 09 2020
STATUS
approved