A391756 Powers k^m, m > 1, of even k that are not perfect powers.

36, 100, 144, 196, 216, 324, 400, 484, 576, 676, 784, 900, 1000, 1156, 1296, 1444, 1600, 1728, 1764, 1936, 2116, 2304, 2500, 2704, 2744, 2916, 3136, 3364, 3600, 3844, 4356, 4624, 4900, 5184, 5476, 5776, 5832, 6084, 6400, 6724, 7056, 7396, 7744, 7776, 8000, 8100

Offset

1,1

Comments

Powers k^m, m > 1, of even k in A007916.

Even terms in A131605.

Disjoint union of A390956, A391320, and A391376.

A075090 is the union of this sequence and A000079.

A390010 is the union of this sequence and A390952.

A131605 is the union of this sequence and A216419 (odd terms in A131605).

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Index entries for sequences related to powerful numbers.

Example

Table of n, a(n) for n = 1..12:
 n   a(n)
----------------------------------
 1    36 =  6^2 = 2^2 *  3^2
 2   100 = 10^2 = 2^2 *  5^2
 3   144 = 12^2 = 2^4 *  3^2
 4   196 = 14^2 = 2^2 *  7^2
 5   216 =  6^3 = 2^3 *  3^3
 6   324 = 18^2 = 2^2 *  3^4
 7   400 = 20^2 = 2^4 *  5^2
 8   484 = 22^2 = 2^2 * 11^2
 9   576 = 24^2 = 2^6 *  3^2
10   676 = 26^2 = 2^2 * 13^2
11   784 = 28^2 = 2^4 *  7^2
12   900 = 30^2 = 2^2 *  3^2 * 5^2

Mathematica

With[{nn = 10000}, Union@ Flatten@ Table[If[And[EvenQ[#1], Length[#2] > 1, GCD @@ #2 > 1] & @@ {#, FactorInteger[#][[;; , -1]]}, #1, Nothing] &[a^2*b^3], {b, Surd[nn, 3]}, {a, Sqrt[nn/b^3] } ] ]

Crossrefs

Cf. A000079, A001597, A001694, A007916, A075090, A126706, A131605, A216419, A286708, A390010, A390952, A390956, A391320, A391376.

Sequence in context: A377817 A131605 A390823 * A376119 A387254 A296204

Adjacent sequences: A391753 A391754 A391755 * A391757 A391758 A391759

Keyword

nonn,easy

Author

Michael De Vlieger, Dec 18 2025

Status

approved