|
|
A355582
|
|
a(n) is the largest 5-smooth divisor of n.
|
|
8
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
LINKS
|
|
|
FORMULA
|
Multiplicative with a(p^e) = p^e if p <= 5 and 1 otherwise.
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)
|
|
CROSSREFS
|
Cf. A006519, A007814, A007949, A038500, A051037, A060904, A065331, A112765, A165725, A355583, A355584.
|
|
KEYWORD
|
nonn,mult,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|