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A086568 Smallest number having as many distinct prime factors as n has prime factors, when counted with multiplicity. 3
1, 2, 2, 6, 2, 6, 2, 30, 6, 6, 2, 30, 2, 6, 6, 210, 2, 30, 2, 30, 6, 6, 2, 210, 6, 6, 30, 30, 2, 30, 2, 2310, 6, 6, 6, 210, 2, 6, 6, 210, 2, 30, 2, 30, 30, 6, 2, 2310, 6, 30, 6, 30, 2, 210, 6, 210, 6, 6, 2, 210, 2, 6, 30, 30030, 6, 30, 2, 30, 6, 30, 2, 2310, 2, 6, 30, 30, 6, 30, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

a(n) = n if and only if n = A002110(m) for some m. That is, primorials give the fixed points of this sequence.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..2310

Index entries for sequences computed from exponents in factorization of n

FORMULA

a(n) = prime(bigomega(n))# = A002110(A001222(n)).

For all n >= 1, A001221(a(n)) = A001222(a(n)) = A001222(n).

MATHEMATICA

Array[Times @@ Prime@ Range@ PrimeOmega@ # &, 79] (* Michael De Vlieger, Sep 25 2017 *)

PROG

(PARI)

A002110(n) = prod(i=1, n, prime(i));

A086568(n) = A002110(bigomega(n)); \\ Antti Karttunen, Jul 07 2017

CROSSREFS

Cf. A001221, A001222, A002110, A130675, A292586.

Sequence in context: A278162 A187223 A175194 * A239074 A160122 A093656

Adjacent sequences:  A086565 A086566 A086567 * A086569 A086570 A086571

KEYWORD

nonn

AUTHOR

Reinhard Zumkeller, Jan 03 2004

EXTENSIONS

Formula corrected and comments edited by Antti Karttunen, Jul 07 2017

STATUS

approved

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Last modified December 5 12:04 EST 2021. Contains 349557 sequences. (Running on oeis4.)