A392423 Powers k^m, m > 1, odd k that are neither squarefree nor squareful.

2025, 3969, 5625, 9801, 13689, 18225, 21609, 23409, 29241, 30625, 35721, 42849, 60025, 68121, 75625, 77841, 88209, 91125, 99225, 105625, 110889, 123201, 131769, 136161, 140625, 149769, 164025, 178929, 180625, 210681, 225625, 227529, 245025, 250047, 257049, 263169

Offset

1,1

Comments

Intersection of A005408 and A386762.

Powers k^m, m > 1, of k in A391025.

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    2025 =  45^2 = 3^4 *  5^2
 2    3969 =  63^2 = 3^4 *  7^2
 3    5625 =  75^2 = 3^2 *  5^4
 4    9801 =  99^2 = 3^4 * 11^2
 5   13689 = 117^2 = 3^4 * 13^2
 6   18225 = 135^2 = 3^6 *  5^2
 7   21609 = 147^2 = 3^2 *  7^4
 8   23409 = 153^2 = 3^4 * 17^2
 9   29241 = 171^2 = 3^4 * 19^2
10   30625 = 175^2 = 5^4 *  7^2
11   35721 = 189^2 = 3^6 *  7^2
19   99225 = 315^2 = 3^4 *  5^2 * 7^2

Mathematica

nn = 300000; i = 1; MapIndexed[Set[S[First[#2]], #1] &, Select[Range[1, Sqrt[nn], 2], 1 == Min[#] < Max[#] &@ FactorInteger[#][[All, -1]] &] ]; Union@ Reap[While[j = 2; While[S[i]^j < nn, Sow[S[i]^j]; j++]; j > 2, i++] ][[-1, 1]]

Crossrefs

Cf. A001597, A001694, A005408, A013929, A024619, A126706, A131605, A286708, A332785, A386762, A391025, A392424.

Sequence in context: A126172 A183999 A360216 * A250811 A350869 A031768

Adjacent sequences: A392420 A392421 A392422 * A392424 A392425 A392426

Keyword

nonn,easy

Author

Michael De Vlieger, Jan 10 2026

Status

approved