A375072 Biquadratefree numbers (A046100) that are not cubefree (A004709).

8, 24, 27, 40, 54, 56, 72, 88, 104, 108, 120, 125, 135, 136, 152, 168, 184, 189, 200, 216, 232, 248, 250, 264, 270, 280, 296, 297, 312, 328, 343, 344, 351, 360, 375, 376, 378, 392, 408, 424, 440, 456, 459, 472, 488, 500, 504, 513, 520, 536, 540, 552, 568, 584, 594, 600

Offset

1,1

Comments

Subsequence of A176297 and first differs from it at n = 41: A176297(41) = 432 = 2^4 * 3^3 is not a term of this sequence.

Numbers whose prime factorization has least one exponent that equals 3 and no higher exponent.

Numbers k such that A051903(k) = 3.

The asymptotic density of this sequence is 1/zeta(4) - 1/zeta(3) = A215267 - A088453 = 0.0920310303408826983406... .

Links

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

Index entries for sequences computed from exponents in factorization of n.

Mathematica

Select[Range[600], Max[FactorInteger[#][[;; , 2]]] == 3 &]

Prog

(PARI) is(k) = k > 1 && vecmax(factor(k)[, 2]) == 3;
(Python)
from sympy import mobius, integer_nthroot
def A375072(n):
    def f(x): return n+x-sum(mobius(k)*(x//k**4-x//k**3) for k in range(1, integer_nthroot(x, 4)[0]+1))+sum(mobius(k)*(x//k**3) for k in range(integer_nthroot(x, 4)[0]+1, integer_nthroot(x, 3)[0]+1))
    m, k = n, f(n)
    while m != k:
        m, k = k, f(k)
    return m # Chai Wah Wu, Aug 05 2024

Crossrefs

Intersection of A046100 and A176297.

Cf. A004709, A051903, A067259.

Cf. A002117, A013662, A088453, A215267.

Sequence in context: A366761 A336593 A176297 * A175496 A048109 A068781

Adjacent sequences: A375069 A375070 A375071 * A375073 A375074 A375075

Keyword

nonn,easy

Author

Amiram Eldar, Jul 29 2024

Status

approved