A387377 In the prime factorization of n, replace 2's with 3's, replace 3's with 5's and replace 5's with 2's.

1, 3, 5, 9, 2, 15, 7, 27, 25, 6, 11, 45, 13, 21, 10, 81, 17, 75, 19, 18, 35, 33, 23, 135, 4, 39, 125, 63, 29, 30, 31, 243, 55, 51, 14, 225, 37, 57, 65, 54, 41, 105, 43, 99, 50, 69, 47, 405, 49, 12, 85, 117, 53, 375, 22, 189, 95, 87, 59, 90, 61, 93, 175, 729, 26

Offset

1,2

Comments

This is a multiplicative permutation of the positive integers with order 3.

Links

Paolo Xausa, Table of n, a(n) for n = 1..10000

Formula

a(n) = A181351(A064614(n)).

From Amiram Eldar, Oct 01 2025: (Start)

Dirichlet g.f.: zeta(s-1) * (2^s-2)*(3^s-3)*(5^s-5) / ((2^s-3)*(3^s-5)*(5^s-2)).

Sum_{k=1..n} a(k) ~ (30/23) * n^2. (End)

Example

For example, for n = 6, we have 2 * 3 which becomes 3 * 5 = 15.

Mathematica

A387377[n_] := n*Times @@ ({3/2, 5/3, 2/5}^IntegerExponent[n, {2, 3, 5}]);
Array[A387377, 100] (* Paolo Xausa, Sep 30 2025, after Andrew Howroyd *)

Prog

(PARI) a(n)={my(i=valuation(n, 2), j=valuation(n, 3), k=valuation(n, 5)); n*(3/2)^i*(5/3)^j*(2/5)^k} \\ Andrew Howroyd, Sep 25 2025
(Python)
def A387377(n):
    v2, v3, v5 = (~n & n-1).bit_length(), 0, 0
    m = n>>v2
    q, r = divmod(m, 5)
    while not r:
        m = q
        v5 += 1
        q, r = divmod(m, 5)
    q, r = divmod(m, 3)
    while not r:
        m = q
        v3 += 1
        q, r = divmod(m, 3)
    return m*3**v2*5**v3<<v5 # Chai Wah Wu, Oct 01 2025

Crossrefs

Cf. A064614, A181351.

Sequence in context: A225594 A210946 A319984 * A303772 A200510 A388782

Adjacent sequences: A387374 A387375 A387376 * A387378 A387379 A387380

Keyword

nonn,mult,easy

Author

Cade Spaulding, Sep 25 2025

Status

approved