cp's OEIS Frontend

A050374 Number of ordered factorizations of n into composite factors.

%I A050374 #25 Jan 03 2021 15:31:45
%S A050374 1,0,0,1,0,1,0,1,1,1,0,1,0,1,1,2,0,1,0,1,1,1,0,3,1,1,1,1,0,1,0,3,1,1,
%T A050374 1,4,0,1,1,3,0,1,0,1,1,1,0,5,1,1,1,1,0,3,1,3,1,1,0,5,0,1,1,5,1,1,0,1,
%U A050374 1,1,0,7,0,1,1,1,1,1,0,5,2,1,0,5,1,1,1,3,0,5,1,1,1,1,1,10,0,1,1,4,0,1
%N A050374 Number of ordered factorizations of n into composite factors.
%C A050374 a(n) depends only on prime signature of n (cf. A025487). So a(24) = a(375) since 24 = 2^3*3 and 375 = 3*5^3 both have prime signature (3,1).
%C A050374 The Dirichlet inverse is given by A005171, all but the first term in A005171 turned negative. - _R. J. Mathar_, Jul 15 2010
%H A050374 Antti Karttunen, <a href="/A050374/b050374.txt">Table of n, a(n) for n = 1..16384</a>
%H A050374 <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F A050374 Dirichlet g.f.: 1/(1-B(s)) where B(s) is D.g.f. of characteristic function of composite numbers.
%F A050374 a(n) = A050375(A101296(n)). - _R. J. Mathar_, May 26 2017
%F A050374 For n >= 1, a(p^n) = A000045(n-1), for any prime p.
%F A050374 For n >= 0, a(A002110(n)) = A032032(n).
%p A050374 read(transforms):
%p A050374 [1, seq(-A005171(n), n=2..100)] ;
%p A050374 a050374 := DIRICHLETi(%) ; # _R. J. Mathar_, May 26 2017
%o A050374 (PARI) A050374(n) = if(1==n,n,sumdiv(n,d,if(d<n,!isprime(n/d)*A050374(d),0))); \\ _Antti Karttunen_, Oct 20 2017
%Y A050374 Cf. A002033, A002808, A005171, A050370-A050375, A000045, A002110, A032032.
%K A050374 nonn
%O A050374 1,16
%A A050374 _Christian G. Bower_, Nov 15 1999