%I A034876
%S A034876 0,0,0,1,0,1,0,1,1,2,0,1,0,0,0,2,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,1,0,0,0,
%T A034876 1,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,0,0,
%U A034876 0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,2,0,0,0,0,0,0,0,0,0
%N A034876 Number of ways to write n! as a product of smaller factorials each greater 
               than 1.
%C A034876 By definition, a(n)>0 if and only if n is a member of A034878. If n>2, 
               then a(n!)>max(a(n),a(n!-1)), as (n!)!=n!*(n!-1)!. Similarly, a(A001013(n))>
               0 for n>2. Clearly a(n)=0 if n is a prime A000040. So a(n+1)=1 if 
               n=2^p-1 is a Mersenne prime A000668, as (n+1)!=(2!)^p*n! and n is 
               prime. - Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 15 
               2004
%D A034876 R. K. Guy, Unsolved Problems in Number Theory, B23.
%H A034876 <a href="Sindx_Fa.html#factorial">Index entries for sequences related 
               to factorial numbers</a>.
%H A034876 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               FactorialProducts.html">Factorial Products</a>
%e A034876 a(10)=2 because 10!=3!*5!*7!=6!*7! are the only two ways to write 10! 
               as a product of smaller factorials > 1.
%Y A034876 Cf. A034878, A001013, A075082.
%Y A034876 Sequence in context: A161520 A070097 A096271 this_sequence A091393 A110270 
               A123635
%Y A034876 Adjacent sequences: A034873 A034874 A034875 this_sequence A034877 A034878 
               A034879
%K A034876 easy,nonn,nice
%O A034876 1,10
%A A034876 Erich Friedman (erich.friedman(AT)stetson.edu)
%E A034876 Corrected by Jonathan Sondow (jsondow(AT)alumni.princeton.edu), Dec 18 
               2004