A393947 - OEIS

%I #7 Mar 15 2026 21:53:53

%S 180,252,300,396,450,468,588,612,684,700,720,828,882,980,1008,1044,

%T 1080,1100,1116,1200,1260,1300,1332,1452,1476,1512,1548,1575,1584,

%U 1620,1692,1700,1872,1900,1908,1980,2028,2100,2124,2156,2178,2196,2205,2268,2300,2340

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

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

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

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

%H Michael De Vlieger, <a href="/A393947/b393947.txt">Table of n, a(n) for n = 1..10000</a>

%F {a(n)} = A332785 \ A393946.

%e Let s = A332785.

%e Table of n, a(n) for select n:

%e    n                a(n)

%e --------------------------------------------------

%e    1      s(52) =   180 = 2^2 * 3^2 *  5

%e    2      s(74) =   252 = 2^2 * 3^2 *  7

%e    3      s(90) =   300 = 2^2 * 3   *  5^2

%e    4     s(125) =   396 = 2^2 * 3^2 * 11

%e    5     s(141) =   450 = 2   * 3^2 *  5^2

%e   17     s(371) =  1080 = 2^3 * 3^3 *  5

%e   21     s(434) =  1260 = 2^2 * 3^2 *  5   * 7

%e   28     s(546) =  1575 = 3^2 * 5^2 *  7

%e  339    s(4733) = 12600 = 2^3 * 3^2 *  5^2 * 7

%e  381    s(5218) = 13860 = 2^2 * 3^2 *  5   * 7 * 11

%e 1138   s(14454) = 37800 = 2^3 * 3^3 *  5^2 * 7

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

%Y Cf. A393946.

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

%K nonn

%O 1,1

%A _Michael De Vlieger_, Mar 08 2026