A389144 Weak numbers k such that lpf(k)^2 | k, where lpf(n) denotes the least prime factor of n (A020639).

12, 20, 24, 28, 40, 44, 45, 48, 52, 56, 60, 63, 68, 76, 80, 84, 88, 92, 96, 99, 104, 112, 116, 117, 120, 124, 132, 135, 136, 140, 148, 152, 153, 156, 160, 164, 168, 171, 172, 175, 176, 180, 184, 188, 189, 192, 204, 207, 208, 212, 220, 224, 228, 232, 236, 240, 244

Offset

1,1

Comments

Intersection of A283050 and A052485.

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

A283050 is the union of this sequence and A001694.

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).

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

Links

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

Example

Let s = A332785.
a(1) = s(1) = 12 = 2^2 * 3.
s(2) = 18 is not divisible by 2^2, thus not in this sequence.
a(2) = s(3) = 20 = 2^2 * 5.
a(3) = s(4) = 24 = 2^3 * 3.
a(4) = s(5) = 28 = 2^2 * 7.
a(5) = s(6) = 40 = 2^3 * 5.
a(6) = s(7) = 44 = 2^2 * 11.
a(7) = s(8) = 45 = 3^2 * 5.
a(8) = s(9) = 48 = 2^4 * 3.
s(10) = 50 is not divisible by 2^2, thus not a term, etc.

Mathematica

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

Crossrefs

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

Sequence in context: A362620 A112769 A360253 * A097320 A332956 A386417

Adjacent sequences: A389141 A389142 A389143 * A389145 A389146 A389147

Keyword

nonn,easy

Author

Michael De Vlieger, Sep 24 2025

Status

approved