A229336 - OEIS

%I #12 Jan 22 2023 17:28:51

%S 1,6,12,5040,30,77598259200,56,1307674368000,168480,12703122432000,

%T 132,

%U 52875224823823084892891318660312910903645116196873830400000000000000,182,440505199411200,493242753024000,8222838654177922817725562880000000,306

%N Product of sums of elements of nonempty subsets of divisors of n.

%C Number of nonempty subsets of divisors of n = A100587(n).

%F a(2^n)  = (2^(n+1) - 1)!.

%e For n = 2^2 = 4; divisors of 4: {1, 2, 4}; nonempty subsets of divisors of n: {1}, {2}, {4}, {1, 2}, {1, 4}, {2, 4}, {1, 2, 4}; product of sums of elements of subsets = 1*2*4*3*5*6*7 = 5040 = (2^3 - 1)! = 7!.

%t Table[Times@@(Total/@Rest[Subsets[Divisors[n]]]),{n,20}] (* _Harvey P. Dale_, Jan 22 2023 *)

%Y Cf. A229335 (sum of sums of elements of nonempty subsets of divisors of n),

%Y A229337 (sum of products of elements of nonempty subsets of divisors of n),

%Y A229338 (product of products of elements of nonempty subsets of divisors of n).

%K nonn

%O 1,2

%A _Jaroslav Krizek_, Sep 20 2013