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

8, 16, 27, 32, 54, 64, 81, 108, 125, 128, 162, 216, 243, 250, 256, 324, 343, 375, 432, 486, 500, 512, 625, 648, 686, 729, 750, 864, 972, 1000, 1024, 1029, 1125, 1250, 1296, 1331, 1372, 1458, 1500, 1715, 1728, 1875, 1944, 2000, 2048, 2058, 2187, 2197, 2250, 2401, 2500

Offset: 1

Author

Amiram Eldar, May 30 2022

Keywords

• nonn

Comments

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

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

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Subsequence of A070003.

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

Cf. A006530, A071178.

Programs

Mathematica

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

Python

from sympy import factorint
def c(n, e): f = factorint(n); return f[max(f)] >= e
def ok(n): return n > 1 and c(n, 3)
print([k for k in range(2501) if ok(k)]) # Michael S. Branicky, May 30 2022