A285634 a(1) = 4, a(n) = Product_{d|a(n-1)} d.

4, 8, 64, 2097152, 3450873173395281893717377931138512726225554486085193277581262111899648

Offset: 1

Author

Ilya Gutkovskiy, Apr 23 2017

Keywords

• nonn
• easy

Comments

Iterating the product-of-divisors function.

The next term is too large to include.

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).

The next term has 8067 digits. - Harvey P. Dale, Apr 18 2019

Examples

			a(1) = 4;
a(2) = 8 because 4 has 3 divisors {1, 2, 4} and 1*2*4 = 8;
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.
...
a(6) = 2^26796;
a(7) = 2^359026206;
a(8) = 2^64449908476890321;
a(9) = 2^2076895351339769460477611370186681, etc.
		

Links

• Eric Weisstein's World of Mathematics, Divisor Product

Crossrefs

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

Programs

Mathematica

RecurrenceTable[{a[1] == 4, a[n] == Sqrt[a[n - 1]]^DivisorSigma[0, a[n - 1]]}, a, {n, 5}]
NestList[Times@@Divisors[#]&,4,4] (* Harvey P. Dale, Apr 18 2019 *)

Formula

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

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