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URL: https://oeis.org/A381951

⇱ A381951 - OEIS

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A381951
Nonsquarefree odd numbers whose prime factorization has an odd maximum exponent.
2
27, 125, 135, 189, 243, 297, 343, 351, 375, 459, 513, 621, 675, 783, 837, 875, 945, 999, 1029, 1107, 1125, 1161, 1215, 1269, 1323, 1331, 1375, 1431, 1485, 1593, 1625, 1647, 1701, 1715, 1755, 1809, 1917, 1971, 2079, 2125, 2133, 2187, 2197, 2241, 2295, 2375, 2403, 2457
OFFSET
1,1
COMMENTS
Nonsquarefree odd numbers k such that A051903(k) is odd, or equivalently, odd numbers k such that A051903(k) is an odd number that is larger than 1.
The asymptotic density of this sequence is (1/2) * Sum_{k>=3} (-1)^(k+1) * (1 - 2^k/((2^k-1)*zeta(k))) = 0.019098071299657074975... .
LINKS
EXAMPLE
125 = 5^3 is a term since it is odd, divisible by a square (25, and thus it is nonsquarefree), and the maximum exponent in its prime factorization is 3, which is odd.
MATHEMATICA
q[n_] := n > 1 && OddQ[n]; Select[Range[1, 2500, 2], q[Max[FactorInteger[#][[;; , 2]]]] &]
PROG
(PARI) isok(k) = k > 1 && k % 2 && apply(x -> (x > 1 && x % 2), vecmax(factor(k)[, 2]));
CROSSREFS
Intersection of A005408 and A376142.
Complement of A381950 within A013929.
Cf. A051903.
Sequence in context: A232025 A209505 A275430 * A145555 A293894 A137800
KEYWORD
nonn,easy
AUTHOR
Amiram Eldar, Mar 11 2025
STATUS
approved