# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a303278 Showing 1-1 of 1 %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, Table of n, a(n) for n = 1..4096 %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 # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE