A390289 Cubefree numbers that are not prime powers.

6, 10, 12, 14, 15, 18, 20, 21, 22, 26, 28, 30, 33, 34, 35, 36, 38, 39, 42, 44, 45, 46, 50, 51, 52, 55, 57, 58, 60, 62, 63, 65, 66, 68, 69, 70, 74, 75, 76, 77, 78, 82, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 98, 99, 100, 102, 105, 106, 110, 111, 114, 115, 116, 117

Offset

1,1

Comments

Numbers with more than 1 distinct prime factor whose set of prime exponents is a subset of {1,2}.

Intersection of A004709 and A024619.

Union of A120944 and A391023, disjoint sets.

Union of A120944, A177492, and A386684, disjoint sets.

Union of A067259 \ A001248 and A120944.

This sequence is A377880 \ A000961.

Links

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

Example

Table of n, a(n) for select n:
 n   a(n)
---------------------
 1     6 = 2   *  3
 2    10 = 2   *  5
 3    12 = 2^2 *  3
 4    14 = 2   *  7
 5    15 = 3   *  5
 6    18 = 2   *  3^2
 7    20 = 2^2 *  5
 8    21 = 3   *  7
 9    22 = 2   * 11
10    26 = 2   * 13
16    36 = 2^2 *  3^2
55   100 = 2^2 *  5^2

Mathematica

Select[Range[120], And[Length[#] > 1, SubsetQ[{1, 2}, Union[#]]] &[FactorInteger[#][[All, -1]] ] &]

Prog

(Python)
from math import isqrt
from sympy import mobius, integer_nthroot, primepi
def A390289(n):
    def f(x): return n+x+1-sum(mobius(k)*(x//k**3) for k in range(1, integer_nthroot(x, 3)[0]+1))+primepi(x)+primepi(isqrt(x))
    m, k = n, f(n)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Jan 07 2026

Crossrefs

Cf. A001248, A004709, A024619, A067259, A120944, A177492, A377880, A386684, A391023.

Sequence in context: A084227 A299992 A237051 * A340749 A296205 A325281

Adjacent sequences: A390286 A390287 A390288 * A390290 A390291 A390292

Keyword

nonn,easy

Author

Michael De Vlieger, Dec 31 2025

Status

approved