A062513 - OEIS

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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, 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