|
%I #23 Jan 03 2021 15:07:38
%S 1,1,1,2,1,2,1,3,2,2,1,5,1,2,2,6,1,5,1,5,2,2,1,10,2,2,3,5,1,6,1,10,2,
%T 2,2,14,1,2,2,10,1,6,1,5,5,2,1,22,2,5,2,5,1,10,2,10,2,2,1,18,1,2,5,18,
%U 2,6,1,5,2,6,1,32,1,2,5,5,2,6,1,22,6,2,1,18,2,2,2,10,1,18,2,5,2,2,2
%N Number of ordered factorizations of n into members of A050376.
%C 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).
%H Antti Karttunen, <a href="/A050379/b050379.txt">Table of n, a(n) for n = 1..65537</a>
%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>
%F Dirichlet g.f.: 1/(1-B(s)) where B(s) is D.g.f. of characteristic function of A050376.
%F a(p^k) = A023359(k), for any prime p.
%F a(A002110(n)) = A000142(n) = n!.
%F a(n) = A050380(A101296(n)). - _R. J. Mathar_, May 26 2017
%p read(transforms) :
%p L := [1] :
%p for n from 2 to 100 do
%p if isA050376(n) then
%p L := [op(L),-1] ;
%p else
%p L := [op(L),0] ;
%p end if;
%p end do :
%p a050379 := DIRICHLETi(L) ; # _R. J. Mathar_, May 26 2017
%o (PARI)
%o A064547(n) = {my(f = factor(n)[, 2]); sum(k=1, #f, hammingweight(f[k])); } \\ _Michel Marcus_, Feb 10 2016
%o isA050376(n) = ((1==omega(n)) && (1==A064547(n))); \\ Checking that omega(n) is 1 is just an optimization here.
%o A050379(n) = if(1==n,n,sumdiv(n,d,if(d<n,isA050376(n/d)*A050379(d),0))); \\ _Antti Karttunen_, Oct 20 2017
%Y Cf. A002033, A050376, A050377, A050378, A050380.
%Y Cf. also A000142, A002110, A023359.
%K nonn
%O 1,4
%A _Christian G. Bower_, Nov 15 1999
|
