|
%I #20 Sep 21 2023 01:45:02
%S 1,1,1,8,1,1,1,4,27,1,1,8,1,1,1,32,1,27,1,8,1,1,1,4,125,1,9,8,1,1,1,
%T 16,1,1,1,216,1,1,1,4,1,1,1,8,27,1,1,32,343,125,1,8,1,9,1,4,1,1,1,8,1,
%U 1,27,128,1,1,1,8,1,1,1,108,1,1,125,8,1,1,1,32,243,1,1,8,1,1,1,4,1,27,1,8,1,1
%N In the prime factorization of n, increment even powers and decrement odd powers (multiplicative).
%H Reinhard Zumkeller, <a href="/A011264/b011264.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = Product_{k=1..A001221(n)} (A027748(n,k)^A004442(A124010(n,k))). - _Reinhard Zumkeller_, Jun 23 2013
%F From _Amiram Eldar_, Jan 07 2023: (Start)
%F a(n) = n^2/A011262(n).
%F a(n) = n*A007947(n)/A007913(n)^2.
%F a(n) = n*A336643(n)/A007913(n).
%F a(n) = A356191(n)/A007913(n). (End)
%F Dirichlet g.f.: zeta(2*s-2) * Product_{p prime} (1 + 1/p^s + 1/p^(2*s-3) - 1/p^(2*s-2)). - _Amiram Eldar_, Sep 21 2023
%t f[n_, k_] := n^(If[EvenQ[k], k + 1, k - 1]); Table[Times @@ f @@@ FactorInteger[n], {n, 94}] (* _Jayanta Basu_, Aug 14 2013 *)
%o (Haskell)
%o a011264 n = product $ zipWith (^)
%o (a027748_row n) (map a004442 $ a124010_row n)
%o -- _Reinhard Zumkeller_, Jun 23 2013
%o (PARI) a(n) = {my(f = factor(n)); prod(i = 1, #f~, f[i,1]^if(f[i,2]%2, f[i,2]-1, f[i,2]+1));} \\ _Amiram Eldar_, Jan 07 2023
%Y Cf. A001221, A004442, A007913, A007947, A011262, A027748, A336643, A356191.
%K easy,nonn,mult
%O 1,4
%A _Marc LeBrun_
|
