The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 60th year, we have over 367,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309377 a(n) is the product of the divisors of n^n (A000312). 1
 1, 1, 8, 729, 68719476736, 30517578125, 2444746349972956194083608044935243159422957210683702349648543934214737968217920868940091707112078529114392164827136, 459986536544739960976801, 2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376 (list; graph; refs; listen; history; text; internal format)
 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 4 05:42 EST 2023. Contains 367541 sequences. (Running on oeis4.)