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

1,1

Comments

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

Complement of A036966.

Links

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Example

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

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A068937 A285316 A378287 * A361395 A390538 A329135

Adjacent sequences: A362144 A362145 A362146 * A362148 A362149 A362150

Keyword

nonn

Author

Bernard Schott, Apr 09 2023

Status

approved