A390290 Powers k^m, m > 1, such that k is in A303946 and are products of primorials.

144, 576, 1728, 2304, 3600, 5184, 9216, 13824, 14400, 20736, 32400, 36864, 57600, 82944, 110592, 129600, 147456, 176400, 186624, 216000, 230400, 248832, 331776, 373248, 518400, 589824, 705600, 746496, 884736, 921600, 1166400, 1327104, 1587600, 1728000, 2073600

Offset

1,1

Comments

Intersection of A389864 and A025487 = A368682 \ A365308.

Union of disjoint subsequences A389260 and A389397.

A389312 is the union of this sequence and A380452.

A368682 is the union of this sequence and A365308, both disjoint.

A364930 is the union of this sequence, A365308, and A378002, all disjoint.

A364710 is the union of this sequence, A365308, A378002, and A386223, all disjoint.

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     144 =  12^2 = 2^4  * 3^2
 2     576 =  24^2 = 2^6  * 3^2
 3    1728 =  12^3 = 2^6  * 3^3
 4    2304 =  48^2 = 2^8  * 3^2
 5    3600 =  60^2 = 2^4  * 3^2 * 5^2
 6    5184 =  72^2 = 2^6  * 3^4
 7    9216 =  96^2 = 2^10 * 3^2
 8   13824 =  24^3 = 2^9  * 3^3
 9   14400 = 120^2 = 2^6  * 3^2 * 5^2
10   20736 =  12^4 = 2^8  * 3^4
11   32400 = 180^2 = 2^4  * 3^4 * 5^2
12   36864 = 192^2 = 2^12 * 3^2

Mathematica

nn = 2^21; mm = Sqrt[nn]; i = 1; k = 2; fQ[x_] := And[Length[#] > 1, CountDistinct[#[[;; , -1]] ] > 1, Times @@ MapIndexed[Prime[First[#2] ]^#1 &, ReverseSort[#[[;; , -1]] ] ] == x] &[FactorInteger[x] ]; MapIndexed[Set[S[First[#2]], #1] &, Select[Range[mm], fQ] ]; 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, A002110, A025487, A055932, A126706, A286708, A364710, A365308, A368682, A378002, A380452, A386223, A389260, A389312, A389397, A389864.

Sequence in context: A017522 A180413 A396551 * A389397 A137885 A204398

Adjacent sequences: A390287 A390288 A390289 * A390291 A390292 A390293

Keyword

nonn

Author

Michael De Vlieger, Nov 02 2025

Status

approved