%I #6 May 27 2017 12:53:40

%S 1,1,1,1,1,3,1,1,1,3,1,6,1,3,3,1,1,6,1,6,3,3,1,10,1,3,1,6,1,16,1,1,3,

%T 3,3,20,1,3,3,10,1,16,1,6,6,3,1,15,1,6,3,6,1,10,3,10,3,3,1,50,1,3,6,1,

%U 3,16,1,6,3,16,1,50,1,3,6,6,3,16,1,15,1,3,1,50,3,3,3,10,1,50

%N Count of Mosaic numbers that equal n.

%C The number of solutions x to A000026(x)=n.

%H R. J. Mathar, <a href="/A191278/b191278.txt">Table of n, a(n) for n = 1..1000</a>

%F Let n=product_j p_j^e(j) be the prime factorization of n and beta=A073093(n). Then a(n)*beta = product_j binomial(beta,e(j)). [Gordon-Robertson in A000026, Theorem 1]

%p A191278 := proc(n)

%p local f, beta, a, j ;

%p f := ifactors(n)[2] ;

%p beta := A073093(n) ;

%p a := 1/beta ;

%p for j in ifactors(n)[2] do

%p a := a*binomial(beta, op(2, j) ) ;

%p end do:

%p a ;

%p end proc:

%K nonn,easy

%O 1,6

%A _R. J. Mathar_, May 29 2011