cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

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%I A309377 #17 Jun 27 2022 16:22:52
%S A309377 1,1,8,729,68719476736,30517578125,
%T A309377 2444746349972956194083608044935243159422957210683702349648543934214737968217920868940091707112078529114392164827136,
%U A309377 459986536544739960976801,2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376
%N A309377 a(n) is the product of the divisors of n^n (A000312).
%C A309377 Subset of A007955.
%e A309377 a(0) = 1 because 0^0 = 1, whose only divisor is 1, so the product of divisors is 1.
%e A309377 a(1) = 1 because 1^1 = 1, so the product of divisors is 1.
%e A309377 a(3) = 729 because 3^3 = 27, whose divisors are (1, 3, 9, 27), and their product is 729.
%o A309377 (SageMath)
%o A309377 [ product((1*i^i).divisors()) for i in range(10) ]
%o A309377 (Magma) [&*Divisors(n^n): n in [0..8]]; // _Marius A. Burtea_, Jul 26 2019
%o A309377 (Python)
%o A309377 from math import isqrt, prod
%o A309377 from sympy import factorint
%o A309377 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
%Y A309377 Cf. A007955, A062727.
%K A309377 nonn
%O A309377 0,3
%A A309377 _Hauke Löffler_, Jul 26 2019