A217854 Product of all divisors of n, positive or negative.

-1, 4, 9, -64, 25, 1296, 49, 4096, -729, 10000, 121, 2985984, 169, 38416, 50625, -1048576, 289, 34012224, 361, 64000000, 194481, 234256, 529, 110075314176, -15625, 456976, 531441, 481890304, 841, 656100000000, 961, 1073741824, 1185921

Offset: 1

Author

Franklin T. Adams-Watters, Oct 19 2012

Keywords

• sign

Comments

a(n) is negative iff n is a square.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000005, A062758, A158387, A363657, A363658.

Programs

Mathematica

a[n_] := (-n)^DivisorSigma[0, n]; Array[a, 33] (* Amiram Eldar, Aug 31 2023 *)

PARI

a(n) = (-n)^numdiv(n); \\ Michel Marcus, Aug 31 2023

Formula

a(n) = (-n)^tau(n) = (-n)^A000005(n).

a(n) = A158387(n) * A062758(n). - Andrew Howroyd, Aug 31 2023