A381950 Odd numbers whose prime factorization has an even maximum exponent.

1, 9, 25, 45, 49, 63, 75, 81, 99, 117, 121, 147, 153, 169, 171, 175, 207, 225, 245, 261, 275, 279, 289, 315, 325, 333, 361, 363, 369, 387, 405, 423, 425, 441, 475, 477, 495, 507, 525, 529, 531, 539, 549, 567, 575, 585, 603, 605, 625, 637, 639, 657, 693, 711, 725

Offset

1,2

Comments

Odd numbers k such that A051903(k) is even.

The asymptotic density of this sequence is (1/2) * Sum_{k>=2} (-1)^k * (1 - 2^k/((2^k-1)*zeta(k))) = 0.075617194130991839249... .

Links

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

Example

9 = 3^2 is a term since it is odd and 2 is even.
45 = 3^2 * 5 is a term since it is odd and 2 is even.
125 = 5^3 is not a term since 3 is odd.

Mathematica

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

Prog

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

Crossrefs

Intersection of A005408 and A368714.

Subsequence of A381956.

A381823 is a subsequence.

Cf. A051903, A375039, A381951.

Sequence in context: A227518 A031036 A371086 * A381823 A348749 A291259

Adjacent sequences: A381947 A381948 A381949 * A381951 A381952 A381953

Keyword

nonn,easy

Author

Amiram Eldar, Mar 11 2025

Status

approved