This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A153823 #19 Sep 08 2022 08:45:40
%S A153823 0,0,1,3,7,15,29,59,95,159,269,539,791,1583,2591,4031,5375,10751,
%T A153823 14687,29375,41039,60799,95999,191999,242879,340031,532223,677375,
%U A153823 917279,1834559,2332799,4665599,5529599,7864319,12165119,16422911
%N A153823 Number of proper divisors of n!.
%C A153823 a(n) is the number of proper divisors of factorial number A000142(n).
%H A153823 G. C. Greubel, <a href="/A153823/b153823.txt">Table of n, a(n) for n = 0..1000</a>
%F A153823 a(n) = A000005(A000142(n)) - 1 = A032741(A000142(n)) = A027423(n) - 1.
%e A153823 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
%t A153823 Table[DivisorSigma[0, n!] - 1, {n, 0, 50}] (* _G. C. Greubel_, Aug 30 2016 *)
%o A153823 (Magma) [DivisorSigma(0,Factorial(n)) - 1: n in [0..40]]; // _Vincenzo Librandi_, Aug 31 2016
%o A153823 (PARI) a(n) = numdiv(n!) - 1; \\ _Michel Marcus_, Aug 31 2016
%o A153823 (Python)
%o A153823 from sympy import factorial, divisor_count
%o A153823 def A153823(n):
%o A153823 return divisor_count(factorial(n))-1 # _Chai Wah Wu_, Aug 24 2020
%Y A153823 Cf. A000005, A000142, A027423, A032741.
%Y A153823 Cf. A153823, A153825. [From _Omar E. Pol_, Jan 17 2009]
%K A153823 nonn
%O A153823 0,4
%A A153823 _Omar E. Pol_, Jan 02 2009
%E A153823 More terms from _Omar E. Pol_, Jan 17 2009