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%I #19 Aug 31 2021 04:09:30
%S 1,-2,-3,6,-5,36,-7,-56,36,100,-11,-792,-13,196,225,1820,-17,-2754,
%T -19,-3800,441,484,-23,48576,300,676,-2925,-10584,-29,-27000,-31,
%U -201376,1089,1156,1225,396900,-37,1444,1521,395200,-41,-74088,-43,-41624,-44550
%N If n = Product (p_j^k_j) then a(n) = Product ((-1)^k_j * binomial(n, k_j)).
%H Seiichi Manyama, <a href="/A341837/b341837.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = A346148(n, n). - _Sebastian Karlsson_, Aug 22 2021
%t a[1] = 1; a[n_] := Times @@ ((-1)^#[[2]] Binomial[n, #[[2]]] &/@ FactorInteger[n]); Table[a[n], {n, 45}]
%o (PARI) a(n) = my(f=factor(n)[,2]); prod(k=1, #f, (-1)^f[k]*binomial(n, f[k])); \\ _Michel Marcus_, Feb 21 2021
%Y Cf. A007427, A007428, A008683, A163767, A247343, A341831, A341832, A341833, A341834, A341835, A341836.
%Y Cf. A346148.
%K sign
%O 1,2
%A _Ilya Gutkovskiy_, Feb 21 2021