cp's OEIS Frontend

A303278 If n = Product_j p_j^k_j where the p_j are distinct primes then a(n) = (Product_j k_j)^(Product_j p_j).

%I A303278 #12 May 01 2021 09:55:41
%S A303278 1,1,1,4,1,1,1,9,8,1,1,64,1,1,1,16,1,64,1,1024,1,1,1,729,32,1,27,
%T A303278 16384,1,1,1,25,1,1,1,4096,1,1,1,59049,1,1,1,4194304,32768,1,1,4096,
%U A303278 128,1024,1,67108864,1,729,1,4782969,1,1,1,1073741824,1,1,2097152,36,1,1,1,17179869184,1,1,1,46656,1,1,32768
%N A303278 If n = Product_j p_j^k_j where the p_j are distinct primes then a(n) = (Product_j k_j)^(Product_j p_j).
%C A303278 This is different from A008477, which is Product_j k_j^p_j. - _N. J. A. Sloane_, May 01 2021
%H A303278 Antti Karttunen, <a href="/A303278/b303278.txt">Table of n, a(n) for n = 1..4096</a>
%F A303278 a(n) = tau(n/rad(n))^rad(n) = A005361(n)^A007947(n).
%F A303278 a(p^k) = k^p where p is a prime.
%F A303278 a(A000142(k)) = A135291(k)^A034386(k).
%e A303278 a(36) = a(2^2 * 3^2) = (2*2)^(2*3) = 4^6 = 4096.
%t A303278 Table[Times@@Transpose[FactorInteger[n]][[2]]^Last[Select[Divisors[n], SquareFreeQ]], {n, 75}]
%o A303278 (PARI) a(n) = my(f=factor(n)); factorback(f[, 2])^factorback(f[, 1]); \\ _Michel Marcus_, Apr 21 2018
%Y A303278 Cf. A000026, A000142, A005117 (indices of ones), A005361, A007947, A008477, A034386, A039696, A135291, A285769, A303277.
%K A303278 nonn
%O A303278 1,4
%A A303278 _Ilya Gutkovskiy_, Apr 20 2018
%E A303278 Definition clarified by _N. J. A. Sloane_, May 01 2021