A157672 Number of unordered factorizations of n! into two distinct proper factors.

0, 1, 3, 7, 14, 29, 47, 79, 134, 269, 395, 791, 1295, 2015, 2687, 5375, 7343, 14687, 20519, 30399, 47999, 95999, 121439, 170015, 266111, 338687, 458639, 917279, 1166399, 2332799, 2764799, 3932159, 6082559, 8211455, 9797759, 19595519

Offset: 2

Author

Jaume Oliver Lafont, Mar 04 2009, Mar 05 2009

Keywords

• nonn

Crossrefs

Cf. A157612.

Programs

Mathematica

Table[Times@@(Last/@FactorInteger[ n! ]+1)/2-1,{n,2,40}] (* Ray Chandler, Mar 07 2009 *)

PARI

for(k=2,40,print1(numdiv(k!)/2-1,", "))

Python

from math import prod
from collections import Counter
from sympy import factorint
def A157672(n): return prod(e+1 for e in sum((Counter(factorint(i)) for i in range(2,n+1)),start=Counter()).values())//2-1 # Chai Wah Wu, Jun 25 2022

Formula

For n > 1, a(n) = A027423(n)/2 - 1. - Ray Chandler, Mar 07 2009

Extensions

Extended by Ray Chandler, Mar 07 2009

PARI program rewritten Jaume Oliver Lafont, Mar 09 2009