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A087652 Product of the nonprime divisors of n. 4
1, 1, 1, 4, 1, 6, 1, 32, 9, 10, 1, 288, 1, 14, 15, 512, 1, 972, 1, 800, 21, 22, 1, 55296, 25, 26, 243, 1568, 1, 27000, 1, 16384, 33, 34, 35, 1679616, 1, 38, 39, 256000, 1, 74088, 1, 3872, 6075, 46, 1, 42467328, 49, 12500, 51, 5408, 1, 1417176, 55, 702464, 57, 58 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,4

LINKS

Michel Marcus, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = 1 if n=1 or n is prime; a(n) = n if n=1 or n is semiprime (A001358).

From Wesley Ivan Hurt, Jun 08 2020: (Start)

a(n) = Product_{d|n, d nonprime} d.

If n is squarefree, then a(n) = n^(d(n)/2-1), where d(n) is the number of divisors of n (A000005). (End)

a(p^e) = p^((e^2+e-2)/2) for p prime, e > 0. - Bernard Schott, Jun 08 2020

EXAMPLE

n=12: nonprime divisors = {4,6,12}: a(12) = 4*6*12 = 288.

PROG

(PARI) a(n) = my(p=1); fordiv(n, d, if (!isprime(d), p*=d)); p; \\ Michel Marcus, Aug 05 2017

CROSSREFS

Cf. A000005, A023890, A033273.

Sequence in context: A197008 A344442 A316223 * A072195 A032310 A032220

Adjacent sequences: A087649 A087650 A087651 * A087653 A087654 A087655

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Sep 25 2003

STATUS

approved

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Last modified January 27 03:13 EST 2023. Contains 359836 sequences. (Running on oeis4.)