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A354561 Numbers divisible by the cube of their largest prime factor.

%I A354561 #16 Jun 01 2022 05:11:54
%S A354561 8,16,27,32,54,64,81,108,125,128,162,216,243,250,256,324,343,375,432,
%T A354561 486,500,512,625,648,686,729,750,864,972,1000,1024,1029,1125,1250,
%U A354561 1296,1331,1372,1458,1500,1715,1728,1875,1944,2000,2048,2058,2187,2197,2250,2401,2500
%N A354561 Numbers divisible by the cube of their largest prime factor.
%C A354561 Numbers k such that P(k)^3 | k, where P(k) = A006530(k).
%C A354561 Numbers k such that A071178(k) >= 3.
%H A354561 Amiram Eldar, <a href="/A354561/b354561.txt">Table of n, a(n) for n = 1..10000</a>
%e A354561 8 is a term since 2^3|8 and 2 is the largest prime factor of 8.
%e A354561 54 = 2*3^3 is a term since 3^3|8 and 3 is the largest prime factor of 54.
%t A354561 Select[Range[2500], FactorInteger[#][[-1, 2]] > 2 &]
%o A354561 (Python)
%o A354561 from sympy import factorint
%o A354561 def c(n, e): f = factorint(n); return f[max(f)] >= e
%o A354561 def ok(n): return n > 1 and c(n, 3)
%o A354561 print([k for k in range(2501) if ok(k)]) # _Michael S. Branicky_, May 30 2022
%Y A354561 Subsequence of A070003.
%Y A354561 Subsequences: A036966 \ {1}, A349306 \ {1}, A354562.
%Y A354561 Cf. A006530, A071178.
%K A354561 nonn
%O A354561 1,1
%A A354561 _Amiram Eldar_, May 30 2022