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Number of factorizations of n into distinct numbers with an odd number of prime factors.
3

%I #12 May 26 2017 04:28:38

%S 1,1,1,0,1,1,1,1,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2,0,1,1,1,1,2,1,1,1,1,

%T 1,2,1,1,1,2,1,2,1,1,1,1,1,2,0,1,1,1,1,2,1,2,1,1,1,3,1,1,1,1,1,2,1,1,

%U 1,2,1,2,1,1,1,1,1,2,1,2,1,1,1,3,1,1,1,2,1,3,1,1,1,1,1,3,1,1,1,2,1,2,1

%N Number of factorizations of n into distinct numbers with an odd number of prime factors.

%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 R. J. Mathar, <a href="/A050332/b050332.txt">Table of n, a(n) for n = 1..2519</a>

%F Dirichlet g.f.: Product_{n is in A026424}(1+1/n^s).

%F a(n) = A050333(A101296(n)). - _R. J. Mathar_, May 26 2017

%Y Cf. A026424, A045778, A050333. a(p^k)=A000700. a(A002110)=A003724.

%K nonn

%O 1,24

%A _Christian G. Bower_, Oct 15 1999