A280581 a(n) = the product of divisors of sum of divisors of n.

1, 3, 8, 7, 36, 1728, 64, 225, 13, 5832, 1728, 21952, 196, 331776, 331776, 31, 5832, 1521, 8000, 3111696, 32768, 10077696, 331776, 46656000000, 31, 3111696, 2560000, 9834496, 810000, 139314069504, 32768, 250047, 254803968, 8503056, 254803968, 8281, 1444

Offset: 1

Author

Jaroslav Krizek, Jan 05 2017

Keywords

• nonn

Comments

a(n) < A007955(n) for numbers n in A219364.

a(n) | A007955(n) for numbers n in A219363.

A007955(n) | a(n) for numbers n in A219362.

n | a(n) for numbers n in A175200.

Examples

			For n = 5; a(n) = product of divisors of sigma(5) = 1*2*3*6 = 36.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..1024
• Index entries for sequences related to sigma(n).

Crossrefs

Cf. A000203, A007955, A219362, A219363, A219364, A280582.

Programs

Magma

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

Mathematica

Table[Times @@ Divisors@ DivisorSigma[1, n], {n, 37}] (* Michael De Vlieger, Jan 06 2017 *)
a[n_] := (s = DivisorSigma[1, n])^(DivisorSigma[0, s]/2); Array[a, 40] (* Amiram Eldar, Jun 26 2022 *)

PARI

a(n) = my(k = 1); fordiv(sigma(n), d, k*=d); k; \\ Michel Marcus, Jan 06 2017

Python

from math import isqrt
from sympy import divisor_count, divisor_sigma
def A280581(n): return (lambda m:isqrt(m)**c if (c:=divisor_count(m)) & 1 else m**(c//2))(divisor_sigma(n)) # Chai Wah Wu, Jun 25 2022

Formula

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