A391376 Powers k^m, m > 1, where k is an even Achilles number.

5184, 11664, 40000, 82944, 153664, 186624, 250000, 373248, 419904, 640000, 746496, 937024, 944784, 1259712, 1327104, 1827904, 1882384, 2458624, 3240000, 3779136, 4000000, 5345344, 6718464, 7290000, 8000000, 8340544, 10240000, 11943936, 12446784, 14992384, 15116544

Offset

1,1

Comments

Intersection of A005843 and A383394 = A386762 \ A391375.

Perfect powers of numbers in A390952.

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 select n:
 n       a(n)
----------------------------------------
 1      5184 =   72^2 = 2^6  * 3^4
 2     11664 =  108^2 = 2^4  * 3^6
 3     40000 =  200^2 = 2^6  * 5^4
 4     82944 =  288^2 = 2^10 * 3^4
 5    153664 =  392^2 = 2^6  * 7^4
 6    186624 =  432^2 = 2^8  * 3^6
 7    250000 =  500^2 = 2^4  * 5^6
 8    373248 =   72^3 = 2^9  * 3^6
 9    419904 =  648^2 = 2^6  * 3^8
10    640000 =  800^2 = 2^10 * 5^4
11    746496 =  864^2 = 2^10 * 3^6
19   3240000 = 1800^2 = 2^6  * 3^4 * 5^4

Mathematica

nn = 1600000; mm = Sqrt[nn]; i = 1; k = 2; MapIndexed[Set[S[First[#2]], #1] &, Union@ Flatten@ Table[If[And[EvenQ[#1], GCD @@ #2 == 1] & @@ {#, FactorInteger[#][[;; , -1]] }, #1, Nothing] &[a^2*b^3], {b, Surd[mm, 3]}, {a, Sqrt[mm/b^3]}]]; Union@ Reap[While[j = 2; While[S[i]^j < nn, Sow[S[i]^j]; j++]; j > 2, k++; i++] ][[-1, 1]]

Crossrefs

Cf. A001597, A001694, A005843, A052486, A126706, A131605, A286708, A383394, A390952, A391375.

Sequence in context: A185485 A061050 A383394 * A390435 A175745 A190464

Adjacent sequences: A391373 A391374 A391375 * A391377 A391378 A391379

Keyword

nonn,easy

Author

Michael De Vlieger, Dec 09 2025

Status

approved