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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, 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
1,30
LINKS
FORMULA
a(n) = A061537(n)/[n^A001221(n)].
a(n) = n^[(A034444(n)/2)-A001221(n)].
EXAMPLE
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.
MATHEMATICA
Table[n^(2^(PrimeNu[n] - 1) - PrimeNu[n]), {n, 1, 50}] (* G. C. Greubel, May 20 2017 *)
PROG
(PARI) for(n=1, 50, print1(round(n^(2^(omega(n) -1) - omega(n))), ", ")) \\ G. C. Greubel, May 20 2017
CROSSREFS
KEYWORD
nonn
AUTHOR
Labos Elemer, Jul 13 2001
STATUS
approved