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

1,2

Links

Table of n, a(n) for n=1..47.

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]

Example

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

Prog

(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

Crossrefs

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

Sequence in context: A194924 A205489 A343935 * A076365 A070971 A338438

Adjacent sequences: A280682 A280683 A280684 * A280686 A280687 A280688

Keyword

nonn,changed

Author

Jaroslav Krizek, Jan 07 2017

Status

approved