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A375072
Biquadratefree numbers (A046100) that are not cubefree (A004709).
2
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... .
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.
Sequence in context: A366761 A336593 A176297 * A175496 A048109 A068781
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Jul 29 2024
STATUS
approved