A387958 Achilles numbers that are not products of primorials.

108, 200, 392, 500, 648, 675, 800, 968, 972, 1125, 1323, 1352, 1372, 1568, 1944, 2000, 2312, 2700, 2888, 3087, 3200, 3267, 3528, 3872, 3888, 4000, 4232, 4500, 4563, 5000, 5292, 5324, 5408, 5488, 6075, 6125, 6272, 6728, 7688, 7803, 8575, 8712, 8748, 8788, 9000

Offset

1,1

Comments

Intersection of A052486 and A369361 = A052486 \ A025487.

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

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    108 = 2^2 *  3^3
 2    200 = 2^3 *  5^2
 3    392 = 2^3 *  7^2
 4    500 = 2^2 *  5^3
 5    648 = 2^3 *  3^4
 6    675 = 3^3 *  5^2
 7    800 = 2^5 *  5^2
 8    968 = 2^3 * 11^2
 9    972 = 2^2 *  3^5
10   1125 = 3^2 *  5^3
18   2700 = 2^2 *  3^3 * 5^2
23   3528 = 2^3 *  3^2 * 7^2

Mathematica

nn = 9000; Rest@ Select[Union@ Flatten@ Table[a^2*b^3, {b, Surd[nn, 3]}, {a, Sqrt[nn/b^3]}], And[GCD @@ #2 == 1, Times @@ MapIndexed[Prime[First[#2]]^#1 &, ReverseSort[#2]] != #1] & @@ {#, FactorInteger[#][[;; , -1]]} &]

Crossrefs

Cf. A001597, A001694, A025487, A052486, A126706, A131605, A286708, A367268, A369361, A369636.

Sequence in context: A338382 A338384 A344702 * A044340 A044721 A095050

Adjacent sequences: A387955 A387956 A387957 * A387959 A387960 A387961

Keyword

nonn

Author

Michael De Vlieger, Oct 12 2025

Status

approved