A062513 Product of unitary divisors of n is divided by n^(number of distinct prime factors).

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 30, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 42, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 60, 1, 1, 1, 1, 1, 66, 1, 1, 1, 70, 1, 1, 1, 1, 1, 1, 1, 78, 1, 1, 1, 1, 1, 84, 1, 1, 1, 1, 1, 90, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Author

Labos Elemer, Jul 13 2001

Keywords

• nonn

Examples

			n=210, with 4 p-divisors; all its 16 divisors are unitary; product=210^(16/2)=3782285936100000000, while 210^4=1944810000; a(210)=3782285936100000000/1944810000=1944810000.
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A000005, A034444, A001221.

Programs

Mathematica

Table[n^(2^(PrimeNu[n] - 1) - PrimeNu[n]), {n,1,50}] (* G. C. Greubel, May 20 2017 *)

PARI

for(n=1,50, print1(round(n^(2^(omega(n) -1) - omega(n))), ", ")) \\ G. C. Greubel, May 20 2017

Formula

a(n) = A061537(n)/[n^A001221(n)].

a(n) = n^[(A034444(n)/2)-A001221(n)].