A108068 Number of ordered pairs (i,j) with i>=0, j>=0 and i!*j! = n.

0, 4, 4, 0, 1, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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

0,2

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

lim sup_{n->infinity} a(n) = 6 [Kane].

Conjecture: max_{n->infinity} a(n) = 6 [Kane].

Example

1 = 0!*0! = 0!*1! = 1!*0! = 1!*1!, so a(1) = 4.

Prog

(Sage)
def A108068(n) :
    count = 0;
    m = 0; factm = 1;
        while factm <= n :
            k = 0; 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. A108069.

Sequence in context: A156450 A067007 A066298 * A283998 A318143 A131124

Adjacent sequences: A108065 A108066 A108067 * A108069 A108070 A108071

Keyword

nonn,easy

Author

N. J. A. Sloane, Jun 04 2005

Extensions

More terms from Christian G. Bower, Jun 04 2005

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

Status

approved