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

1,1

Comments

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

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

Subsequence of A070003.

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

Cf. A006530, A071178.

Sequence in context: A059172 A360558 A107606 * A349306 A245713 A320966

Adjacent sequences: A354558 A354559 A354560 * A354562 A354563 A354564

Keyword

nonn

Author

Amiram Eldar, May 30 2022

Status

approved