1,1

Perfect powers k^m, m > 1, where k is composite and weak (i.e., in A106543) and is not a primorial.

Intersection of A131605 and A369361 = A131605 \ A025487.

Proper subset of A369636, which in turn is a proper subset of A367268.

Superset of A380456.

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

Index entries for sequences related to powerful numbers.

n a(n)

-----------------------------------

1 100 = 10^2 = 2^2 * 5^2

2 196 = 14^2 = 2^2 * 7^2

3 225 = 15^2 = 3^2 * 5^2

4 324 = 18^2 = 2^2 * 3^4

5 400 = 20^2 = 2^4 * 5^2

6 441 = 21^2 = 3^2 * 7^2

7 484 = 22^2 = 2^2 * 11^2

8 676 = 26^2 = 2^2 * 13^2

9 784 = 28^2 = 2^4 * 7^2

10 1000 = 10^3 = 2^3 * 5^3

11 1089 = 33^2 = 3^2 * 11^2

17 1764 = 42^2 = 2^2 * 3^2 * 7^2

nn = 10000; mm = Sqrt[nn]; i = 1; k = 2; fQ[x_] := And[CompositeQ[x], GCD @@ # == 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &, ReverseSort[#]] != x] &@ FactorInteger[x][[;; , -1]]; MapIndexed[Set[S[First[#2]], #1] &, Select[Range@Sqrt[nn], fQ]]; Union@ Reap[While[j = 2; While[S[i]^j < nn, Sow[S[i]^j]; j++]; j > 2, k++; i++]][[-1, 1]]

Cf. A001597, A001694, A002110, A007916, A024619, A106543, A126706, A131605, A286708, A367268, A369361, A369636, A380456.

Sequence in context: A068805 A369417 A231088 * A380456 A365745 A104023

Adjacent sequences: A387617 A387618 A387619 * A387621 A387622 A387623

Michael De Vlieger, Oct 09 2025

approved