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

1,2

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..1024

Index entries for sequences related to sigma(n).

Formula

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

Example

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A122237 A307162 A233418 * A278755 A016625 A019630

Adjacent sequences: A280578 A280579 A280580 * A280582 A280583 A280584

Keyword

nonn

Author

Jaroslav Krizek, Jan 05 2017

Status

approved