editing

approved

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

A073093 := proc(n) local f, beta, j ; f := ifactors(n)[2] ; beta := 1 ; for j from 1 to nops(f) do beta := beta + op(2, op(j, f)) ; end do: beta ; end proc:

A := proc(n) local f, beta, a, j ; f := ifactors(n)[2] ; beta := A073093(n) ; a := 1/beta ; for j in ifactors(n)[2] do a := a*binomial(beta, op(2, j) ) ; end do: a ; end proc:

seq(A(n), n=1..90) ;

A191278 := proc(n)

local f, beta, a, j ;

f := ifactors(n)[2] ;

beta := A073093(n) ;

a := 1/beta ;

for j in ifactors(n)[2] do

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

end do:

a ;

end proc:

approved

editing

_R. J. Mathar (mathar(AT)strw.leidenuniv.nl), _, May 29 2011

proposed

approved

allocated for R. J. Mathar

Count of Mosaic numbers that equal n.

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, 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, 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

1,6

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

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]

A073093 := proc(n) local f, beta, j ; f := ifactors(n)[2] ; beta := 1 ; for j from 1 to nops(f) do beta := beta + op(2, op(j, f)) ; end do: beta ; end proc:

A := proc(n) local f, beta, a, j ; f := ifactors(n)[2] ; beta := A073093(n) ; a := 1/beta ; for j in ifactors(n)[2] do a := a*binomial(beta, op(2, j) ) ; end do: a ; end proc:

seq(A(n), n=1..90) ;

allocated

nonn,easy

R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 29 2011

approved

proposed

allocated for R. J. Mathar

allocated

approved