A341837 If n = Product (p_j^k_j) then a(n) = Product ((-1)^k_j * binomial(n, k_j)).

1, -2, -3, 6, -5, 36, -7, -56, 36, 100, -11, -792, -13, 196, 225, 1820, -17, -2754, -19, -3800, 441, 484, -23, 48576, 300, 676, -2925, -10584, -29, -27000, -31, -201376, 1089, 1156, 1225, 396900, -37, 1444, 1521, 395200, -41, -74088, -43, -41624, -44550

Offset: 1

Author

Ilya Gutkovskiy, Feb 21 2021

Keywords

• sign

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007427, A007428, A008683, A163767, A247343, A341831, A341832, A341833, A341834, A341835, A341836.

Cf. A346148.

Programs

Mathematica

a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[n, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 45}]

PARI

a(n) = my(f=factor(n)[,2]); prod(k=1, #f, (-1)^f[k]*binomial(n, f[k])); \\ Michel Marcus, Feb 21 2021

Formula

a(n) = A346148(n, n). - Sebastian Karlsson, Aug 22 2021