A051119 - OEIS

A051119

a(n) = n/p^k, where p = largest prime dividing n and p^k = highest power of p dividing n.

1, 1, 1, 1, 1, 2, 1, 1, 1, 2, 1, 4, 1, 2, 3, 1, 1, 2, 1, 4, 3, 2, 1, 8, 1, 2, 1, 4, 1, 6, 1, 1, 3, 2, 5, 4, 1, 2, 3, 8, 1, 6, 1, 4, 9, 2, 1, 16, 1, 2, 3, 4, 1, 2, 5, 8, 3, 2, 1, 12, 1, 2, 9, 1, 5, 6, 1, 4, 3, 10, 1, 8, 1, 2, 3, 4, 7, 6, 1, 16, 1, 2, 1, 12, 5, 2, 3, 8, 1, 18, 7, 4, 3, 2, 5, 32, 1, 2, 9, 4, 1

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OFFSET

1,6

LINKS

T. D. Noe, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = n/A053585(n).

EXAMPLE

a(36) = 4 because 36/3^2 = 4, 3^2 is highest power dividing 36 of largest prime dividing 36.

a(50) = 50/5^2 = 2.

MATHEMATICA

f[n_]:=Module[{c=Last[FactorInteger[n]]}, n/First[c]^Last[c]]; Array[ f, 110] (* Harvey P. Dale, Oct 14 2011 *)