login
a(1) = 4, a(n) = Product_{d|a(n-1)} d.
0

%I #6 Apr 18 2019 09:32:07

%S 4,8,64,2097152,

%T 3450873173395281893717377931138512726225554486085193277581262111899648

%N a(1) = 4, a(n) = Product_{d|a(n-1)} d.

%C Iterating the product-of-divisors function.

%C The next term is too large to include.

%C Let a(n) = Product_{d|a(n-1)} d, with a(1) = p^k, p is a prime, k >= 0 and b(n) = b(n-1)*(b(n-1) + 1)/2, with b(1) = k, then a(n) = p^b(n).

%C The next term has 8067 digits. - _Harvey P. Dale_, Apr 18 2019

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DivisorProduct.html">Divisor Product</a>

%F a(1) = 4, a(n) = a(n-1)^(A000005(a(n-1))/2).

%F a(n) = 2^A007501(n-1).

%e a(1) = 4;

%e a(2) = 8 because 4 has 3 divisors {1, 2, 4} and 1*2*4 = 8;

%e a(3) = 64 because 64 has 7 divisors {1, 2, 4, 8, 16, 32, 64} and 1*2*4*8*16*32*64 = 2097152, etc.

%e ...

%e a(6) = 2^26796;

%e a(7) = 2^359026206;

%e a(8) = 2^64449908476890321;

%e a(9) = 2^2076895351339769460477611370186681, etc.

%t RecurrenceTable[{a[1] == 4, a[n] == Sqrt[a[n - 1]]^DivisorSigma[0, a[n - 1]]}, a, {n, 5}]

%t NestList[Times@@Divisors[#]&,4,4] (* _Harvey P. Dale_, Apr 18 2019 *)

%Y Cf. A000005, A000079, A007497, A007501, A007955.

%K nonn,easy

%O 1,1

%A _Ilya Gutkovskiy_, Apr 23 2017