cp's OEIS Frontend

A334740 Number of unordered factorizations of n with 3 different parts > 1.

%I A334740 #16 Jun 14 2020 00:49:37
%S A334740 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,
%T A334740 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,
%U A334740 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
%N A334740 Number of unordered factorizations of n with 3 different parts > 1.
%C A334740 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).
%H A334740 Jacob Sprittulla, <a href="/A334740/b334740.txt">Table of n, a(n) for n = 1..1000</a>
%e A334740 a(48) = 3 = #{ (6,4,2), (8,3,2), (4,3,2,2) }.
%o A334740 (R)
%o A334740 maxe  <- function(n, d)  { i=0; while( n%%(d^(i+1))==0 )  { i=i+1 }; i }
%o A334740 uhRec <- function(n, l=1)  {
%o A334740   uh = 0
%o A334740   if( n<=0 ) {
%o A334740     return(0)
%o A334740   } else if(n==1) {
%o A334740     return(ifelse(l==0, 1, 0))
%o A334740   } else if(l<=0) {
%o A334740     return(0)
%o A334740   } else if( (n>=2) && (l>=1) )  {
%o A334740     for(d in 2:n)  {
%o A334740       m = maxe(n, d)
%o A334740       if(m>=1)  for(i in 1:m)  for(j in 1:min(i, l))   {
%o A334740         uhj = uhRec( n/d^i, l-j )
%o A334740         uh  = uh +  log(d)/log(n) * (-1)^(j+1) * choose(i, j) * uhj
%o A334740       }
%o A334740     }
%o A334740     return(round(uh, 3))
%o A334740   }
%o A334740 }
%o A334740 n=100; l=2; sapply(1:n, uhRec, l)    # A334739
%o A334740 n=100; l=3; sapply(1:n, uhRec, l)    # A334740
%Y A334740 Cf. A334739 (2 different parts), A072670 (2 parts), A122179 (3 parts), A211159 (2 distinct parts), A122180 (3 distinct parts), A001055, A045778
%K A334740 nonn
%O A334740 1,48
%A A334740 _Jacob Sprittulla_, May 09 2020