A362147 Numbers that are not cubefull.

2, 3, 4, 5, 6, 7, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 29, 30, 31, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84

Offset: 1

Author

Bernard Schott, Apr 09 2023

Keywords

• nonn

Comments

Integers m for which there is a prime p that divides m, but p^3 does not divide m.

Complement of A036966.

Examples

			2|24 and 2^3|24, but 3|24 and 3^3 does not divide 24, so 24 is a term.
		

Crossrefs

Cf. A004709 (cubefree), A046099 (not cubefree), A036966 (cubefull), A362148 (non-cubefree that are not cubefull).

Programs

Mathematica

Select[Range[2, 100], Min[FactorInteger[#][[;; , 2]]] < 3 &] (* Amiram Eldar, Apr 09 2023 *)

PARI

isok(k) = (k!=1) && (vecmin(factor(k)[, 2])<=2); \\ Michel Marcus, Apr 12 2023

Python

from math import gcd
from sympy import integer_nthroot, factorint
def A362147(n):
    def f(x):
        c = n
        for w in range(1,integer_nthroot(x,5)[0]+1):
            if all(d<=1 for d in factorint(w).values()):
                for y in range(1,integer_nthroot(z:=x//w**5,4)[0]+1):
                    if gcd(w,y)==1 and all(d<=1 for d in factorint(y).values()):
                        c += integer_nthroot(z//y**4,3)[0]
        return c
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Nov 22 2024