A389145 Weak numbers k such that gpf(k)^2 | k, where gpf(n) denotes the greatest prime factor of n (A006530).

18, 50, 54, 75, 98, 147, 150, 162, 242, 245, 250, 294, 300, 338, 363, 375, 450, 486, 490, 507, 578, 588, 600, 605, 686, 722, 726, 735, 750, 845, 847, 867, 882, 980, 1014, 1029, 1058, 1083, 1176, 1183, 1200, 1210, 1250, 1350, 1445, 1452, 1458, 1470, 1500, 1587

Offset

1,1

Comments

Intersection of A070003 and A052485.

A070003 is the union of this sequence and A001694.

Proper subset of A332785 (i.e., intersection of A052485 and A013929) since squarefree numbers are forbidden in A070003.

This sequence intersects neither A366825 nor A360767, both are proper subsets of A332785.

Note: the union of this sequence and A389144 is missing numbers in A332785.

Links

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

Example

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

Mathematica

Select[Range[1600], And[! Divisible[#1, Apply[Times, #2[[All, 1]] ]^2], #2[[-1, -1]] > 1] & @@ {#, FactorInteger[#]} &]

Crossrefs

Cf. A001694, A006530, A013929, A052485, A070003, A126706, A332785, A360767, A366825, A389144.

Sequence in context: A071365 A360252 A097319 * A258211 A354929 A093617

Adjacent sequences: A389142 A389143 A389144 * A389146 A389147 A389148

Keyword

nonn,easy

Author

Michael De Vlieger, Sep 24 2025

Status

approved