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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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,30

LINKS

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

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

Cf. A000005, A034444, A001221.

Sequence in context: A137348 A137737 A262706 * A040906 A040907 A040908

Adjacent sequences:  A062510 A062511 A062512 * A062514 A062515 A062516

KEYWORD

nonn

AUTHOR

Labos Elemer, Jul 13 2001

STATUS

approved

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Last modified June 24 02:56 EDT 2021. Contains 345415 sequences. (Running on oeis4.)