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A362147 Numbers that are not cubefull.

%I A362147 #34 Nov 22 2024 11:07:37
%S A362147 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,
%T A362147 30,31,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,
%U A362147 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
%N A362147 Numbers that are not cubefull.
%C A362147 Integers m for which there is a prime p that divides m, but p^3 does not divide m.
%C A362147 Complement of A036966.
%e A362147 2|24 and 2^3|24, but 3|24 and 3^3 does not divide 24, so 24 is a term.
%t A362147 Select[Range[2, 100], Min[FactorInteger[#][[;; , 2]]] < 3 &] (* _Amiram Eldar_, Apr 09 2023 *)
%o A362147 (PARI) isok(k) = (k!=1) && (vecmin(factor(k)[, 2])<=2); \\ _Michel Marcus_, Apr 12 2023
%o A362147 (Python)
%o A362147 from math import gcd
%o A362147 from sympy import integer_nthroot, factorint
%o A362147 def A362147(n):
%o A362147     def f(x):
%o A362147         c = n
%o A362147         for w in range(1,integer_nthroot(x,5)[0]+1):
%o A362147             if all(d<=1 for d in factorint(w).values()):
%o A362147                 for y in range(1,integer_nthroot(z:=x//w**5,4)[0]+1):
%o A362147                     if gcd(w,y)==1 and all(d<=1 for d in factorint(y).values()):
%o A362147                         c += integer_nthroot(z//y**4,3)[0]
%o A362147         return c
%o A362147     m, k = n, f(n)
%o A362147     while m != k: m, k = k, f(k)
%o A362147     return m # _Chai Wah Wu_, Nov 22 2024
%Y A362147 Cf. A004709 (cubefree), A046099 (not cubefree), A036966 (cubefull), A362148 (non-cubefree that are not cubefull).
%K A362147 nonn
%O A362147 1,1
%A A362147 _Bernard Schott_, Apr 09 2023