A050347 - OEIS

%I #10 May 26 2017 04:25:26

%S 1,1,1,1,1,4,1,4,1,4,1,10,1,4,4,7,1,10,1,10,4,4,1,26,1,4,4,10,1,22,1,

%T 14,4,4,4,34,1,4,4,26,1,22,1,10,10,4,1,63,1,10,4,10,1,26,4,26,4,4,1,

%U 74,1,4,10,29,4,22,1,10,4,22,1,105,1,4,10,10,4,22,1,63,7,4,1,74,4,4,4,26

%N Number of ways to factor n into distinct factors with 2 levels of parentheses.

%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="/A050347/b050347.txt">Table of n, a(n) for n = 1..2159</a>

%F Dirichlet g.f.: Product_{n>=2}(1+1/n^s)^A050345(n).

%F a(n) = A050348(A101296(n)). - _R. J. Mathar_, May 26 2017

%e 6 = ((6)) = ((3*2)) = ((3)*(2)) = ((3))*((2)).

%Y Cf. A045778, A050345-A050350. a(p^k)=A050343. a(A002110)=A000307.

%K nonn

%O 1,6

%A _Christian G. Bower_, Oct 15 1999