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A153823
Number of proper divisors of n!.
3
0, 0, 1, 3, 7, 15, 29, 59, 95, 159, 269, 539, 791, 1583, 2591, 4031, 5375, 10751, 14687, 29375, 41039, 60799, 95999, 191999, 242879, 340031, 532223, 677375, 917279, 1834559, 2332799, 4665599, 5529599, 7864319, 12165119, 16422911
OFFSET
0,4
COMMENTS
a(n) is the number of proper divisors of factorial number A000142(n).
LINKS
FORMULA
a(n) = A000005(A000142(n)) - 1 = A032741(A000142(n)) = A027423(n) - 1.
EXAMPLE
For n=4, 4! = 4*3*2*1 = 24, which has 7 proper divisors: 1, 2, 3, 4, 6, 8, and 12. So a(4) = 7. - Michael B. Porter, Aug 30 2016
MATHEMATICA
Table[DivisorSigma[0, n!] - 1, {n, 0, 50}] (* G. C. Greubel, Aug 30 2016 *)
PROG
(Magma) [DivisorSigma(0, Factorial(n)) - 1: n in [0..40]]; // Vincenzo Librandi, Aug 31 2016
(PARI) a(n) = numdiv(n!) - 1; \\ Michel Marcus, Aug 31 2016
(Python)
from sympy import factorial, divisor_count
def A153823(n):
return divisor_count(factorial(n))-1 # Chai Wah Wu, Aug 24 2020
CROSSREFS
Cf. A153823, A153825. [From Omar E. Pol, Jan 17 2009]
Sequence in context: A018087 A171625 A284245 * A283007 A283258 A080011
KEYWORD
nonn
AUTHOR
Omar E. Pol, Jan 02 2009
EXTENSIONS
More terms from Omar E. Pol, Jan 17 2009
STATUS
approved