A072195 Replace all prime factors p of n with n/p.

1, 1, 1, 4, 1, 6, 1, 64, 9, 10, 1, 144, 1, 14, 15, 4096, 1, 324, 1, 400, 21, 22, 1, 13824, 25, 26, 729, 784, 1, 900, 1, 1048576, 33, 34, 35, 46656, 1, 38, 39, 64000, 1, 1764, 1, 1936, 2025, 46, 1, 5308416, 49, 2500, 51, 2704, 1, 157464, 55, 175616, 57, 58, 1, 216000, 1

Offset

1,4

Comments

For n>1: a(n)=1 iff n is prime.

Links

Table of n, a(n) for n=1..61.

Formula

a(n) = n^(A001222(n)-1).

Example

a(18) = a(2*3*3) = (18/2)*(18/3)*(18/3) = 9*6*6 = 324.

Mathematica

pf[n_]:=Times@@(n/#&/@Flatten[Table[#[[1]], {#[[2]]}]&/@FactorInteger[ n]]); Array[pf, 70] (* Harvey P. Dale, Dec 11 2013 *)

Crossrefs

Sequence in context: A344442 A316223 A087652 * A032310 A032220 A032145

Adjacent sequences: A072192 A072193 A072194 * A072196 A072197 A072198

Keyword

nonn

Author

Reinhard Zumkeller, Jul 02 2002

Status

approved