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A157672 Number of unordered factorizations of n! into two distinct proper factors. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
2,3
LINKS
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
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

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Last modified February 28 03:01 EST 2024. Contains 370379 sequences. (Running on oeis4.)