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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.)