A284600 - OEIS

%I #21 Apr 29 2021 12:32:48

%S 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,

%T 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,

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

%N a(n) = n/(largest prime power dividing n).

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

%H Robert Israel, <a href="/A284600/b284600.txt">Table of n, a(n) for n = 1..10000</a>

%H Ilya Gutkovskiy, <a href="/A284600/a284600.pdf">Extended graphical example</a>

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

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

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

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

%p f:= n ->  n /max(map(t -> t[1]^t[2], ifactors(n)[2])):

%p f(1):= 1:

%p map(f, [$1..100]); # _Robert Israel_, Apr 09 2017

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

%o (Python)

%o from sympy import lcm

%o def a003418(n): return 1 if n<1 else lcm(range(1, n + 1))

%o def a(n):

%o     m=1

%o     while True:

%o         if a003418(m)%n==0: return m

%o         else: m+=1

%o print([n//a(n) for n in range(1, 101)]) # _Indranil Ghosh_, Apr 04 2017

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

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

%K nonn

%O 1,6

%A _Ilya Gutkovskiy_, Mar 30 2017