A219363 -id:A219363

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A280581

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

+10
3

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

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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.

KEYWORD

nonn

AUTHOR

Jaroslav Krizek, Jan 05 2017

STATUS

approved

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