cp's OEIS Frontend

A337106 Number of nontrivial divisors of n!.

%I A337106 #10 Aug 24 2020 23:15:51
%S A337106 0,0,0,2,6,14,28,58,94,158,268,538,790,1582,2590,4030,5374,10750,
%T A337106 14686,29374,41038,60798,95998,191998,242878,340030,532222,677374,
%U A337106 917278,1834558,2332798,4665598,5529598,7864318,12165118,16422910,19595518,39191038,60466174
%N A337106 Number of nontrivial divisors of n!.
%C A337106 A divisor of n is trivial if it is 1 or n.
%F A337106 a(n) = A000005(n!) - 2 for n > 1.
%F A337106 a(n) = A070824(n!).
%e A337106 The a(3) = 2 through a(5) =14 nontrivial divisions:
%e A337106   6/2  24/2   120/2
%e A337106   6/3  24/3   120/3
%e A337106        24/4   120/4
%e A337106        24/6   120/5
%e A337106        24/8   120/6
%e A337106        24/12  120/8
%e A337106               120/10
%e A337106               120/12
%e A337106               120/15
%e A337106               120/20
%e A337106               120/24
%e A337106               120/30
%e A337106               120/40
%e A337106               120/60
%t A337106 Table[Length[DeleteCases[Divisors[n!],1|n!]],{n,10}]
%o A337106 (Python)
%o A337106 from sympy import factorial, divisor_count
%o A337106 def A337106(n):
%o A337106     return 0 if n <= 1 else divisor_count(factorial(n))-2 # _Chai Wah Wu_, Aug 24 2020
%Y A337106 A070824 counts nontrivial divisors.
%Y A337106 A153823 counts proper divisors of n!.
%Y A337106 A337107 has this sequence as column k = 3.
%Y A337106 A000005 counts divisors.
%Y A337106 A000142 lists factorial numbers.
%Y A337106 A001055 counts factorizations.
%Y A337106 A027423 counts divisors of factorial numbers.
%Y A337106 A067824 counts chains of divisors starting with n.
%Y A337106 A074206 counts chains of divisors from n to 1.
%Y A337106 A076716 counts factorizations of factorial numbers.
%Y A337106 A253249 counts chains of divisors.
%Y A337106 A337071 counts chains of divisors starting with n!.
%Y A337106 A337105 counts chains of divisors from n! to 1.
%Y A337106 Cf. A022559, A124010, A251683, A325617, A336941.
%K A337106 nonn
%O A337106 0,4
%A A337106 _Gus Wiseman_, Aug 23 2020
%E A337106 a(0) from _Chai Wah Wu_, Aug 24 2020