A381823 Odd cubefree numbers that are not squarefree.

9, 25, 45, 49, 63, 75, 99, 117, 121, 147, 153, 169, 171, 175, 207, 225, 245, 261, 275, 279, 289, 315, 325, 333, 361, 363, 369, 387, 423, 425, 441, 475, 477, 495, 507, 525, 529, 531, 539, 549, 575, 585, 603, 605, 637, 639, 657, 693, 711, 725, 735, 747, 765, 775

Offset

1,1

Comments

Numbers whose prime factorization has only odd primes, exponents that are smaller than 3 and at least one exponent that equals 2.

Odd numbers k such that A051903(k) = A375039((k+1)/2) = 2.

The asymptotic density of this sequence is 4/(7*zeta(3)) - 2/(3*zeta(2)) = 0.070090906905338896329... .

In general, the asymptotic density of odd k-free numbers (numbers that are not divisible by a k-th power other than 1) that are not (k-1)-free, for k >= 2, is 2^(k-1)/((2^k-1) * zeta(k)) - 2^(k-2)/((2^(k-1)-1) * zeta(k-1)).

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Mathematica

Select[Range[1, 1000, 2], Max[FactorInteger[#][[;; , 2]]] == 2 &]

Prog

(PARI) isok(k) = k % 2 && if(k == 1, 0, vecmax(factor(k)[, 2]) == 2);

Crossrefs

Intersection of A005408 and A067259.

Complement of A056911 within A381822.

Cf. A002117, A013661, A051903, A375039.

Subsequence of A048103.

Sequence in context: A031036 A371086 A381950 * A348749 A291259 A051132

Adjacent sequences: A381820 A381821 A381822 * A381824 A381825 A381826

Keyword

nonn,easy

Author

Amiram Eldar, Mar 08 2025

Status

approved