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

2,3

Links

Table of n, a(n) for n=2..37.

Formula

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A157612.

Sequence in context: A266625 A151754 A192065 * A125899 A266791 A052997

Adjacent sequences: A157669 A157670 A157671 * A157673 A157674 A157675

Keyword

nonn

Author

Jaume Oliver Lafont, Mar 04 2009, Mar 05 2009

Extensions

Extended by Ray Chandler, Mar 07 2009

PARI program rewritten Jaume Oliver Lafont, Mar 09 2009

Status

approved