A108069 Number of ordered pairs (i,j) with i>=1, j>=1 and i!*j! = n.

0, 1, 2, 0, 1, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0

Offset

0,3

Links

Eric M. Schmidt, Table of n, a(n) for n = 0..10000

D. M. Kane, On the number of ways of writing T as a product of factorials, Integers: Electronic Journal of Combinatorial Number Theory, 5 (2005), #A02, 10pp.

Formula

Conjecture: max_{n->infinity} a(n) = 4 [Kane].

Example

1 = 1!*1!, so a(1) = 1; 2 = 1!*2! = 2!*1!, so a(2) = 2. - corrected by Eric M. Schmidt, Dec 07 2012

Prog

(SageMath)
def A108069(n) :
    count = 0;
    m = 1; factm = 1;
    while factm <= n :
        k = 1; factk = 1;
        while factm * factk <= n :
            if factm * factk == n :
                count += 1;
            k += 1; factk *= k;
        m += 1; factm *= m;
    return count; # Eric M. Schmidt, Dec 07 2012

Crossrefs

Cf. A108068.

Sequence in context: A357119 A357883 A091728 * A227837 A263099 A254001

Adjacent sequences: A108066 A108067 A108068 * A108070 A108071 A108072

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 04 2005

Extensions

More terms from Christian G. Bower, Jun 04 2005

a(0) term added by Eric M. Schmidt, Dec 07 2012

Status

approved