A309377 a(n) is the product of the divisors of n^n (A000312).

1, 1, 8, 729, 68719476736, 30517578125, 2444746349972956194083608044935243159422957210683702349648543934214737968217920868940091707112078529114392164827136, 459986536544739960976801, 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376

Offset: 0

Author

Hauke Löffler, Jul 26 2019

Keywords

• nonn

Comments

Subset of A007955.

Examples

			a(0) = 1 because 0^0 = 1, whose only divisor is 1, so the product of divisors is 1.
a(1) = 1 because 1^1 = 1, so the product of divisors is 1.
a(3) = 729 because 3^3 = 27, whose divisors are (1, 3, 9, 27), and their product is 729.
		

Crossrefs

Cf. A007955, A062727.

Programs

Magma

[&*Divisors(n^n): n in [0..8]]; // Marius A. Burtea, Jul 26 2019

Python

from math import isqrt, prod
from sympy import factorint
def A309377(n): return (isqrt(n**n) if (c:=prod(n*e+1 for e in factorint(n).values())) & 1 else 1)*n**(n*(c//2)) # Chai Wah Wu, Jun 25 2022

SageMath

[ product((1*i^i).divisors()) for i in range(10) ]