A375072 - OEIS

%I #14 Aug 06 2024 02:13:34

%S 8,24,27,40,54,56,72,88,104,108,120,125,135,136,152,168,184,189,200,

%T 216,232,248,250,264,270,280,296,297,312,328,343,344,351,360,375,376,

%U 378,392,408,424,440,456,459,472,488,500,504,513,520,536,540,552,568,584,594,600

%N Biquadratefree numbers (A046100) that are not cubefree (A004709).

%C 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.

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

%C Numbers k such that A051903(k) = 3.

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

%H Amiram Eldar, <a href="/A375072/b375072.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Eu#epf">Index entries for sequences computed from exponents in factorization of n</a>.

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

%o (PARI) is(k) = k > 1 && vecmax(factor(k)[,2]) == 3;

%o (Python)

%o from sympy import mobius, integer_nthroot

%o def A375072(n):

%o     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))

%o     m, k = n, f(n)

%o     while m != k:

%o         m, k = k, f(k)

%o     return m # _Chai Wah Wu_, Aug 05 2024

%Y Intersection of A046100 and A176297.

%Y Cf. A004709, A051903, A067259.

%Y Cf. A002117, A013662, A088453, A215267.

%K nonn,easy

%O 1,1

%A _Amiram Eldar_, Jul 29 2024