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

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

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

Mathematica

a[n_] := n^2 * Times @@ FactorInteger[n][[;; , 1]]; Array[a, 50] (* Amiram Eldar, Jun 18 2022 *)

Prog

(PARI) a(n) = n^2 * factorback(factor(n)[, 1]);

Crossrefs

The range of values is A335988.

Cf. A007947, A064549, A065463, A102631, A356191.

Sequence in context: A056824 A367804 A361268 * A297868 A051760 A213519

Adjacent sequences: A355035 A355036 A355037 * A355039 A355040 A355041

Keyword

nonn,easy,mult

Author

Peter Munn, Jun 16 2022

Status

approved