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A284600 a(n) = n/(largest prime power dividing n). 7
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 (list; graph; refs; listen; history; text; internal format)
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: A025865 A085091 A052128 * A114536 A330692 A138010

Adjacent sequences:  A284597 A284598 A284599 * A284601 A284602 A284603

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Mar 30 2017

STATUS

approved

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Last modified February 18 21:20 EST 2020. Contains 332028 sequences. (Running on oeis4.)