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A191278 Count of Mosaic numbers that equal n.

%I A191278 #6 May 27 2017 12:53:40
%S A191278 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 A191278 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 A191278 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 A191278 Count of Mosaic numbers that equal n.
%C A191278 The number of solutions x to A000026(x)=n.
%H A191278 R. J. Mathar, <a href="/A191278/b191278.txt">Table of n, a(n) for n = 1..1000</a>
%F A191278 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 A191278 := proc(n)
%p A191278     local f, beta, a, j ;
%p A191278     f := ifactors(n)[2] ;
%p A191278     beta := A073093(n) ;
%p A191278     a := 1/beta ;
%p A191278     for j in ifactors(n)[2] do
%p A191278         a := a*binomial(beta, op(2, j) ) ;
%p A191278     end do:
%p A191278     a ;
%p A191278 end proc:
%K A191278 nonn,easy
%O A191278 1,6
%A A191278 _R. J. Mathar_, May 29 2011