A284600 a(n) = n/(largest prime power dividing n).

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 3, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 3, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 5, 4, 1, 2, 3, 5, 1, 6, 1, 4, 5, 2, 1, 3, 1, 2, 3, 4, 1, 2, 5, 7, 3, 2, 1, 12, 1, 2, 7, 1, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 5, 1, 2, 1, 12, 5, 2, 3, 8, 1, 10

Offset

1,6

Comments

a(n) = smallest positive number k such that n/k is a prime power.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Ilya Gutkovskiy, Extended graphical example

Formula

a(n) = n/A034699(n).

a(n) = 1 if n is a prime power (A000961).

a(n) = 2 if n is a twice odd prime power (A278568).

Example

a(12) = 3 because 12 = 2^2*3 therefore 12/(largest prime power dividing 12) = 12/4 = 3.

Maple

f:= n ->  n /max(map(t -> t[1]^t[2], ifactors(n)[2])):
f(1):= 1:
map(f, [$1..100]); # Robert Israel, Apr 09 2017

Mathematica

Join[{1}, Table[n/Last[Select[Divisors[n], PrimePowerQ[#1] &]], {n, 2, 90}]]

Prog

(Python)
from sympy import lcm
def a003418(n): return 1 if n<1 else lcm(range(1, n + 1))
def a(n):
    m=1
    while True:
        if a003418(m)%n==0: return m
        else: m+=1
print([n//a(n) for n in range(1, 101)]) # Indranil Ghosh, Apr 04 2017

Crossrefs

Cf. A000961, A003557, A007913, A034699, A052126, A121289, A278568.

Has same beginning as A052128 and A114536 but is strictly different from those two sequences.

Sequence in context: A085091 A345994 A052128 * A114536 A330692 A349658

Adjacent sequences: A284597 A284598 A284599 * A284601 A284602 A284603

Keyword

nonn

Author

Ilya Gutkovskiy, Mar 30 2017

Status

approved