A389144 - OEIS

%I #14 Sep 26 2025 08:44:42

%S 12,20,24,28,40,44,45,48,52,56,60,63,68,76,80,84,88,92,96,99,104,112,

%T 116,117,120,124,132,135,136,140,148,152,153,156,160,164,168,171,172,

%U 175,176,180,184,188,189,192,204,207,208,212,220,224,228,232,236,240,244

%N Weak numbers k such that lpf(k)^2 | k, where lpf(n) denotes the least prime factor of n (A020639).

%C Intersection of A283050 and A052485.

%C Proper subset of A332785 (i.e., intersection of A052485 and A013929) since squarefree numbers are forbidden in A283050.

%C A283050 is the union of this sequence and A001694.

%C Superset of A366825 (i.e., numbers of the form lpf(k)*k, with squarefree k such that omega(k) > 1, where lpf = A020639 and rad = A007947).

%C Note: the union of this sequence and A389145 is missing numbers in A332785.

%H Michael De Vlieger, <a href="/A389144/b389144.txt">Table of n, a(n) for n = 1..10000</a>

%e Let s = A332785.

%e a(1) = s(1) = 12 = 2^2 * 3.

%e s(2) = 18 is not divisible by 2^2, thus not in this sequence.

%e a(2) = s(3) = 20 = 2^2 * 5.

%e a(3) = s(4) = 24 = 2^3 * 3.

%e a(4) = s(5) = 28 = 2^2 * 7.

%e a(5) = s(6) = 40 = 2^3 * 5.

%e a(6) = s(7) = 44 = 2^2 * 11.

%e a(7) = s(8) = 45 = 3^2 * 5.

%e a(8) = s(9) = 48 = 2^4 * 3.

%e s(10) = 50 is not divisible by 2^2, thus not a term, etc.

%t Select[Range[250], And[! Divisible[#1, Apply[Times, #2[[All, 1]] ]^2], #2[[1, -1]] > 1] & @@ {#, FactorInteger[#]} &]

%Y Cf. A001694, A007947, A013929, A020639, A052485, A126706, A283050, A332785, A366825, A389145.

%K nonn,easy

%O 1,1

%A _Michael De Vlieger_, Sep 24 2025