A191278 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

Offset: 1

Author

R. J. Mathar, May 29 2011

Keywords

• nonn
• easy

Comments

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

Links

• R. J. Mathar, Table of n, a(n) for n = 1..1000

Programs

Maple

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:

Formula

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]