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

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

Offset

0,3

Comments

Subset of A007955.

Links

Table of n, a(n) for n=0..8.

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) ]
(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

Crossrefs

Cf. A007955, A062727.

Sequence in context: A115590 A134923 A144230 * A110039 A271741 A254857

Adjacent sequences: A309374 A309375 A309376 * A309378 A309379 A309380

Keyword

nonn

Author

Hauke Löffler, Jul 26 2019

Status

approved