

A309377


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


1



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

0,3


COMMENTS



LINKS



EXAMPLE

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.


PROG

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


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



