A355038 a(n) = n^2 times the squarefree kernel of n.
1, 8, 27, 32, 125, 216, 343, 128, 243, 1000, 1331, 864, 2197, 2744, 3375, 512, 4913, 1944, 6859, 4000, 9261, 10648, 12167, 3456, 3125, 17576, 2187, 10976, 24389, 27000, 29791, 2048, 35937, 39304, 42875, 7776, 50653, 54872, 59319, 16000, 68921, 74088, 79507, 42592, 30375
Offset: 1
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000
Programs
-
Mathematica
a[n_] := n^2 * Times @@ FactorInteger[n][[;; , 1]]; Array[a, 50] (* Amiram Eldar, Jun 18 2022 *)
-
PARI
a(n) = n^2 * factorback(factor(n)[,1]);
Formula
Multiplicative with a(p^e) = p^(2e+1).
a(n) = n^2 * A007947(n).
a(n) = A064549(n^2). - Amiram Eldar, Jun 20 2022
Sum_{k=1..n} a(k) ~ c * n^4, where c = (1/4) * Product_{p prime} (1 - 1/(p*(p+1))) = A065463 / 4 = 0.1761105502... . - Amiram Eldar, Nov 13 2022
a(n) = A356191(n^2). - Amiram Eldar, Nov 30 2023