cp's OEIS Frontend

A280685 a(n) = sum of the divisors of the product of the divisors of n.

%I A280685 #23 Mar 09 2025 12:42:22
%S A280685 1,3,4,15,6,91,8,127,40,217,12,5080,14,399,403,2047,18,16395,20,19812,
%T A280685 741,931,24,991111,156,1281,1093,50800,30,2929531,32,65535,1729,2149,
%U A280685 1767,30203052,38,2667,2379,6397171,42,10506551,44,185928,170508,3871,48
%N A280685 a(n) = sum of the divisors of the product of the divisors of n.
%F A280685 a(n) = A000203(A007955(n)).
%F A280685 a(p) = p + 1 for p = primes (A000040).
%F A280685 a(2^n) = 2*A007955(2^n) - 1. [corrected by _Jason Yuen_, Mar 08 2025]
%e A280685 For n = 4; a(n) = sigma (1*2*4) = sigma(8) = 15.
%o A280685 (Magma) [&+[d: d in Divisors(&*[d: d in Divisors(n)])]: n in [1..100]];
%o A280685 (Python)
%o A280685 from math import isqrt
%o A280685 from sympy import divisor_sigma
%o A280685 def A280685(n): return divisor_sigma((isqrt(n) if (c:=divisor_count(n)) & 1 else 1)*n**(c//2)) # _Chai Wah Wu_, Jun 25 2022
%Y A280685 Cf. A000040, A000203, A007955, A280582, A280684.
%K A280685 nonn
%O A280685 1,2
%A A280685 _Jaroslav Krizek_, Jan 07 2017