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

1, 3, 4, 15, 6, 91, 8, 127, 40, 217, 12, 5080, 14, 399, 403, 2047, 18, 16395, 20, 19812, 741, 931, 24, 991111, 156, 1281, 1093, 50800, 30, 2929531, 32, 65535, 1729, 2149, 1767, 30203052, 38, 2667, 2379, 6397171, 42, 10506551, 44, 185928, 170508, 3871, 48

Offset: 1

Author

Jaroslav Krizek, Jan 07 2017

Keywords

• nonn

Examples

			For n = 4; a(n) = sigma (1*2*4) = sigma(8) = 15.
		

Crossrefs

Cf. A000040, A000203, A007955, A280582, A280684.

Programs

Magma

[&+[d: d in Divisors(&*[d: d in Divisors(n)])]: n in [1..100]];

Python

from math import isqrt
from sympy import divisor_sigma
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

Formula

a(n) = A000203(A007955(n)).

a(p) = p + 1 for p = primes (A000040).

a(2^n) = 2*A007955(2^n) - 1. [corrected by Jason Yuen, Mar 08 2025]