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A363013
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a(n) is the number of prime factors (counted with multiplicity) of the n-th cubefull number (A036966).
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1
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0, 3, 4, 3, 5, 6, 4, 3, 7, 6, 5, 8, 3, 7, 9, 4, 7, 6, 8, 6, 10, 8, 3, 9, 8, 7, 11, 7, 3, 4, 9, 6, 5, 6, 10, 9, 8, 12, 3, 7, 10, 7, 9, 8, 3, 11, 10, 9, 13, 6, 8, 7, 11, 6, 8, 10, 3, 12, 4, 11, 6, 10, 14, 5, 7, 10, 6, 7, 9, 9, 12, 7, 9, 11, 3, 8, 9, 13, 7, 4, 3
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) >= 3, for n > 1.
Sum_{a(k) < x} a(k) = 3*c*x^(1/3)*log(log(x)) + (3*(B_2 - log(2)) + Sum_{p prime} ((4*p^(1/3)+5)/(p^(5/3)+p^(1/3)+1)))*c*x^(1/3) + O(x^(1/3)/sqrt(log(x))), where B_2 = A083342 and c = A362974 (Jakimczuk and Lalín, 2022).
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MATHEMATICA
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PrimeOmega[Select[Range[10000], # == 1 || Min[FactorInteger[#][[;; , 2]]] > 2 &]]
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PROG
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(PARI) iscubefull(n) = n==1 || vecmin(factor(n)[, 2]) > 2;
apply(bigomega, select(iscubefull, [1..10000]))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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