A355582 a(n) is the largest 5-smooth divisor of n.

1, 2, 3, 4, 5, 6, 1, 8, 9, 10, 1, 12, 1, 2, 15, 16, 1, 18, 1, 20, 3, 2, 1, 24, 25, 2, 27, 4, 1, 30, 1, 32, 3, 2, 5, 36, 1, 2, 3, 40, 1, 6, 1, 4, 45, 2, 1, 48, 1, 50, 3, 4, 1, 54, 5, 8, 3, 2, 1, 60, 1, 2, 9, 64, 5, 6, 1, 4, 3, 10, 1, 72, 1, 2, 75, 4, 1, 6, 1, 80

Offset

1,2

Links

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

Formula

Multiplicative with a(p^e) = p^e if p <= 5 and 1 otherwise.

a(n) = A006519(n) * A038500(n) * A060904(n).

a(n) = 2^A007814(n) * 3^A007949(n) * 5^A112765(n).

a(n) = n / A165725(n).

Dirichlet g.f.: zeta(s)*(2^s-1)*(3^s-1)*(5^s-1)/((2^s-2)*(3^s-3)*(5^s-5)). - Amiram Eldar, Dec 25 2022

Mathematica

a[n_] := Times @@ ({2, 3, 5}^IntegerExponent[n, {2, 3, 5}]); Array[a, 100]

Prog

(PARI) a(n) = 3^valuation(n, 3) * 5^valuation(n, 5) << valuation(n, 2);
(Python)
from sympy import multiplicity as v
def a(n): return 2**v(2, n) * 3**v(3, n) * 5**v(5, n)
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Jul 08 2022

Crossrefs

Cf. A006519, A007814, A007949, A038500, A051037, A060904, A065331, A112765, A132741, A165725, A355583, A355584.

Cf. A379005 (rgs-transform), A379006 (ordinal transform).

Sequence in context: A364500 A280701 A064830 * A160377 A373028 A269165

Adjacent sequences: A355579 A355580 A355581 * A355583 A355584 A355585

Keyword

nonn,mult,easy

Author

Amiram Eldar, Jul 08 2022

Status

approved