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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 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

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Last modified September 18 20:23 EDT 2024. Contains 376002 sequences. (Running on oeis4.)