A391375 Powers k^m, m > 1, where k is an odd Achilles number.

455625, 1265625, 1750329, 9529569, 10673289, 20820969, 36905625, 37515625, 60886809, 73530625, 95004009, 102515625, 141776649, 143496441, 204004089, 228765625, 284765625, 307546875, 390971529, 446265625, 515607849, 673246809, 771895089, 791015625, 864536409, 922640625

Offset

1,1

Comments

Intersection of A005408 and A383394 = A386762 \ A391376.

Perfect powers of numbers in A390953.

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       455625 =   675^2 = 3^6  *  5^4
 2      1265625 =  1125^2 = 3^4  *  5^6
 3      1750329 =  1323^2 = 3^6  *  7^4
 4      9529569 =  3087^2 = 3^4  *  7^6
 5     10673289 =  3267^2 = 3^6  * 11^4
 6     20820969 =  4563^2 = 3^6  * 13^4
 7     36905625 =  6075^2 = 3^10 *  5^4
 8     37515625 =  6125^2 = 5^6  *  7^4
 9     60886809 =  7803^2 = 3^6  * 17^4
10     73530625 =  8575^2 = 5^4  *  7^6
18    307546875 =   675^3 = 3^9  *  5^6
27   1093955625 = 33075^2 = 3^6  *  5^4 * 7^4

Mathematica

nn = 10^9; mm = Sqrt[nn]; i = 1; k = 2; MapIndexed[Set[S[First[#2]], #1] &, Rest@ Union@ Flatten@ Table[If[And[OddQ[#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, A005408, A052486, A126706, A131605, A286708, A383394, A390953, A391376.

Sequence in context: A134888 A237867 A234427 * A205024 A207299 A233926

Adjacent sequences: A391372 A391373 A391374 * A391376 A391377 A391378

Keyword

nonn,easy

Author

Michael De Vlieger, Dec 09 2025

Status

approved