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A370788
Cubefull numbers with an odd number of prime factors (counted with multiplicity).
3
8, 27, 32, 125, 128, 243, 343, 432, 512, 648, 1331, 1728, 2000, 2048, 2187, 2197, 2592, 3125, 3888, 4913, 5000, 5488, 5832, 6859, 6912, 8000, 8192, 10125, 10368, 12167, 15552, 16807, 16875, 19208, 19683, 20000, 21296, 21952, 23328, 24389, 27000, 27648, 27783, 29791
OFFSET
1,1
COMMENTS
Jakimczuk (2024) proved:
The number of terms that do not exceed x is N(x) = c * x^(1/3) / 2 + o(x^(1/3)) where c = A362974.
The relative asymptotic density of this sequence within the cubefull numbers is 1/2.
In general, the relative asymptotic density of the s-full numbers (numbers whose exponents in their prime factorization are all >= s) with an odd number of prime factors (counted with multiplicity) within the s-full numbers is 1/2 when s is odd.
LINKS
MATHEMATICA
q[n_] := Module[{e = FactorInteger[n][[;; , 2]]}, AllTrue[e, # > 2 &] && OddQ[Total[e]]]; Select[Range[30000], q]
PROG
(PARI) is(n) = {my(e = factor(n)[, 2]); n > 1 && vecmin(e) > 2 && vecsum(e)%2; }
CROSSREFS
Intersection of A036966 and A026424.
Complement of A370787 within A036966.
Subsequence of A370786.
Cf. A362974.
Sequence in context: A376173 A335988 A097054 * A304291 A056824 A367804
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 02 2024
STATUS
approved