A393947 Numbers that are neither squarefree nor squareful with prime power factor exponents that are not all pairwise coprime.

180, 252, 300, 396, 450, 468, 588, 612, 684, 700, 720, 828, 882, 980, 1008, 1044, 1080, 1100, 1116, 1200, 1260, 1300, 1332, 1452, 1476, 1512, 1548, 1575, 1584, 1620, 1692, 1700, 1872, 1900, 1908, 1980, 2028, 2100, 2124, 2156, 2178, 2196, 2205, 2268, 2300, 2340

Offset

1,1

Comments

Terms have at least 3 distinct prime factors; proper subset of A390949 (intersection of A000977 and A332785).

Terms have at least 1 prime power factor with exponent 1, and at least 1 prime power factor with exponent that exceeds 1.

Smallest a(n) with m distinct prime factors is 6*A002110(m) with m > 2.

Links

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

Formula

{a(n)} = A332785 \ A393946.

Example

Let s = A332785.
Table of n, a(n) for select n:
   n                a(n)
--------------------------------------------------
   1      s(52) =   180 = 2^2 * 3^2 *  5
   2      s(74) =   252 = 2^2 * 3^2 *  7
   3      s(90) =   300 = 2^2 * 3   *  5^2
   4     s(125) =   396 = 2^2 * 3^2 * 11
   5     s(141) =   450 = 2   * 3^2 *  5^2
  17     s(371) =  1080 = 2^3 * 3^3 *  5
  21     s(434) =  1260 = 2^2 * 3^2 *  5   * 7
  28     s(546) =  1575 = 3^2 * 5^2 *  7
 339    s(4733) = 12600 = 2^3 * 3^2 *  5^2 * 7
 381    s(5218) = 13860 = 2^2 * 3^2 *  5   * 7 * 11
1138   s(14454) = 37800 = 2^3 * 3^3 *  5^2 * 7

Mathematica

fQ[x_] := And[Times @@ # != 1, ! AllTrue[#, # > 1 &], ! CoprimeQ @@ #] &@ FactorInteger[x][[All, -1]]; Select[Range[2400], fQ]

Crossrefs

Cf. A393946.

Supersets: A013929, A024619, A126706, A332785, A390949.

Sequence in context: A030636 A378430 A350372 * A179643 A379098 A160134

Adjacent sequences: A393944 A393945 A393946 * A393948 A393949 A393950

Keyword

nonn

Author

Michael De Vlieger, Mar 08 2026

Status

approved