A354561 - OEIS

%I #16 Jun 01 2022 05:11:54

%S 8,16,27,32,54,64,81,108,125,128,162,216,243,250,256,324,343,375,432,

%T 486,500,512,625,648,686,729,750,864,972,1000,1024,1029,1125,1250,

%U 1296,1331,1372,1458,1500,1715,1728,1875,1944,2000,2048,2058,2187,2197,2250,2401,2500

%N Numbers divisible by the cube of their largest prime factor.

%C Numbers k such that P(k)^3 | k, where P(k) = A006530(k).

%C Numbers k such that A071178(k) >= 3.

%H Amiram Eldar, <a href="/A354561/b354561.txt">Table of n, a(n) for n = 1..10000</a>

%e 8 is a term since 2^3|8 and 2 is the largest prime factor of 8.

%e 54 = 2*3^3 is a term since 3^3|8 and 3 is the largest prime factor of 54.

%t Select[Range[2500], FactorInteger[#][[-1, 2]] > 2 &]

%o (Python)

%o from sympy import factorint

%o def c(n, e): f = factorint(n); return f[max(f)] >= e

%o def ok(n): return n > 1 and c(n, 3)

%o print([k for k in range(2501) if ok(k)]) # _Michael S. Branicky_, May 30 2022

%Y Subsequence of A070003.

%Y Subsequences: A036966 \ {1}, A349306 \ {1}, A354562.

%Y Cf. A006530, A071178.

%K nonn

%O 1,1

%A _Amiram Eldar_, May 30 2022